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Ali AS, Javeed S, Faiz Z, Baleanu D. Mathematical modelling, analysis and numerical simulation of social media addiction and depression. PLoS One 2024; 19:e0293807. [PMID: 38470872 DOI: 10.1371/journal.pone.0293807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Accepted: 10/20/2023] [Indexed: 03/14/2024] Open
Abstract
We formulate a mathematical model of social media addiction and depression (SMAD) in this study. Key aspects, such as social media addiction and depression disease-free equilibrium point (SMADDFEP), social media addiction and depression endemic equilibrium point (SMADEEP), and basic reproduction number (R0), have been analyzed qualitatively. The results indicate that if R0 < 1, the SMADDFEP is locally asymptotically stable. The global asymptotic stability of the SMADDFEP has been established using the Castillo-Chavez theorem. On the other hand, if R0 > 1, the unique endemic equilibrium point (SMADEEP) is locally asymptotically stable by Lyapunov theorem, and the model exhibits a forward bifurcation at R0 = 1 according to the Center Manifold theorem. To examine the model's sensitivity, we calculated the normalized forward sensitivity index and conducted a Partial Rank Correlation Coefficient (PRCC) analysis to describe the influence of parameters on the SMAD. The numerical results obtained using the Fourth-order Runge-Kutta (RK-4) scheme show that increasing the number of addicted individuals leads to an increase in the number of depressed individuals.
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Affiliation(s)
- Abu Safyan Ali
- Department of Mathematics and Computer Science, University of Ferrara, Ferrara, Italy
- Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad, Pakistan
| | - Shumaila Javeed
- Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad, Pakistan
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- Department of Mathematics, Mathematics Research Center, Near East University, Nicosia, Mersin 10, Turkey
| | - Zeshan Faiz
- Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad, Pakistan
| | - Dumitru Baleanu
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
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2
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Bhatter S, Jangid K, Kumawat S, Baleanu D, Purohit SD, Suthar DL. A new investigation on fractionalized modeling of human liver. Sci Rep 2024; 14:1636. [PMID: 38238352 PMCID: PMC10796951 DOI: 10.1038/s41598-024-51430-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 01/04/2024] [Indexed: 01/22/2024] Open
Abstract
This study focuses on improving the accuracy of assessing liver damage and early detection for improved treatment strategies. In this study, we examine the human liver using a modified Atangana-Baleanu fractional derivative based on the mathematical model to understand and predict the behavior of the human liver. The iteration method and fixed-point theory are used to investigate the presence of a unique solution in the new model. Furthermore, the homotopy analysis transform method, whose convergence is also examined, implements the mathematical model. Finally, numerical testing is performed to demonstrate the findings better. According to real clinical data comparison, the new fractional model outperforms the classical integer-order model with coherent temporal derivatives.
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Affiliation(s)
- Sanjay Bhatter
- Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, India
| | - Kamlesh Jangid
- Department of Mathematics, Central University of Rajasthan, Ajmer, India
| | - Shyamsunder Kumawat
- Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, India
| | - Dumitru Baleanu
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- Institute of Space Sciences, Magurele-Bucharest, Romania
| | - Sunil Dutt Purohit
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India
| | - Daya Lal Suthar
- Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Ethiopia.
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Sabir Z, Bhat SA, Raja MAZ, Baleanu D, Amin F, Wahab HA. A scale conjugate neural network approach for the fractional schistosomiasis disease system. Comput Methods Biomech Biomed Engin 2023:1-14. [PMID: 38148628 DOI: 10.1080/10255842.2023.2298717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 12/13/2023] [Indexed: 12/28/2023]
Abstract
This study presents the numerical solutions of the fractional schistosomiasis disease model (SDM) using the supervised neural networks (SNNs) and the computational scaled conjugate gradient (SCG), i.e. SNNs-SCG. The fractional derivatives are used for the precise outcomes of the fractional SDM. The preliminary fractional SDM is categorized as: uninfected, infected with schistosomiasis, recovered through infection, expose and susceptible to this virus. The accurateness of the SNNs-SCG is performed to solve three different scenarios based on the fractional SDM with synthetic data obtained with fractional Adams scheme (FAS). The generated data of FAS is used to execute SNNs-SCG scheme with 81% for training samples, 12% for testing and 7% for validation or authorization. The correctness of SNNs-SCG approach is perceived by the comparison with reference FAS results. The performances based on the error histograms (EHs), absolute error, MSE, regression, state transitions (STs) and correlation accomplish the accuracy, competence, and finesse of the SNNs-SCG scheme.
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Affiliation(s)
- Zulqurnain Sabir
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | | | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, Yunlin, Taiwan, Republic of China
| | - Dumitru Baleanu
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Fazli Amin
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
| | - Hafiz Abdul Wahab
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
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Sabir Z, Baleanu D, E Alhazmi S, Ben Said S. Heuristic computing with active set method for the nonlinear Rabinovich-Fabrikant model. Heliyon 2023; 9:e22030. [PMID: 38034676 PMCID: PMC10682130 DOI: 10.1016/j.heliyon.2023.e22030] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Revised: 10/22/2023] [Accepted: 11/02/2023] [Indexed: 12/02/2023] Open
Abstract
The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10-07 and 10-08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model.
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Affiliation(s)
- Zulqurnain Sabir
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Near East University, Mathematics research center, Nicosia, 99138, North Cyprus, Mersin 10 Turkey
| | - Sharifah E Alhazmi
- Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca, USA
| | - Salem Ben Said
- Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, United Arab Emirates
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Mahmood A, Srivastava HM, Abbas M, Abdullah FA, Othman Mohammed P, Baleanu D, Chorfi N. Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach. Heliyon 2023; 9:e20852. [PMID: 37916109 PMCID: PMC10616149 DOI: 10.1016/j.heliyon.2023.e20852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 10/07/2023] [Accepted: 10/09/2023] [Indexed: 11/03/2023] Open
Abstract
The analytical soliton solutions place a lot of value on birefringent fibres. The major goal of this study is to generate novel forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from optical propagations using birefringent fibres. The (presumably new) extended direct algebraic (EDA) technique is used here to extract a large number of solutions for RKLE. It gives soliton solutions up to thirty-seven, which essentially correspond to all soliton families. This method's ability to determine many sorts of solutions through a single process is one of its key advantages. Additionally, it is simple to infer that the technique employed in this study is really straightforward yet one of the quite effective approaches to solving nonlinear partial differential equations so, this novel extended direct algebraic (EDA) technique may be regarded as a comprehensive procedure. The resulting solutions are found to be hyperbolic, periodic, trigonometric, bright and dark, combined bright-dark, and W-shaped soliton, and these solutions are visually represented by means of 2D, 3D, and density plots. The present study can be extended to investigate several other nonlinear systems to understand the physical insights of the optical propagations through birefringent fibre.
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Affiliation(s)
- Ayesha Mahmood
- Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
| | - Hari Mohan Srivastava
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
- Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
- Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
| | - Muhammad Abbas
- Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
| | - Farah Aini Abdullah
- School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
| | - Pshtiwan Othman Mohammed
- Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
| | - Dumitru Baleanu
- Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
- Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
- Department of Medical Research, China Medical University, Taichung 40402, Taiwan
| | - Nejmeddine Chorfi
- Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Ali KK, Raslan KR, Ibrahim AA, Baleanu D. The nonlocal coupled system of Caputo–Fabrizio fractional q‐integro differential equation. Math Methods in App Sciences 2023. [DOI: 10.1002/mma.9646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 08/14/2023] [Indexed: 09/02/2023]
Abstract
This scheme's main goal is to examine the existence, uniqueness, and continuous dependence of solutions for a nonlinear coupled system of fractional q‐integro‐differential equations involving the derivation and integration of fractional Caputo–Fabrizio. The numerical technique methodology of the proposed problem will be introduced. Proving the existence theorem depends on Schauder's fixed‐point theorem. To drive the numerical method, we use the definitions of the fractional derivative and integral of Caputo–Fabrizio and the q‐integral of the Riemann–Liouville type. Then, the integral part will be treated using the trapezoidal method, and the derivative part will be treated using the forward finite difference method. And therefore, the coupled system will be converted into a system of algebraic equation that will be solved together to get the solutions. Finally, we give two examples to illustrate the effectiveness of the suggested approach.
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Affiliation(s)
- Khalid K. Ali
- Department of Mathematics, Faculty of Science Al‐Azhar University Nasr‐City Cairo Egypt
| | - K. R. Raslan
- Department of Mathematics, Faculty of Science Al‐Azhar University Nasr‐City Cairo Egypt
| | | | - Dumitru Baleanu
- Department of Mathematics Cankaya University Ankara Turkey
- Institute of Space Sciences Magurele‐Bucharest Romania
- Department of Medical Research China Medical University Taichung Taiwan
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Javeed S, Abdeen ZU, Baleanu D. Fractional Modeling of Cancer with Mixed Therapies. FRONT BIOSCI-LANDMRK 2023; 28:174. [PMID: 37664940 DOI: 10.31083/j.fbl2808174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Revised: 06/20/2023] [Accepted: 07/19/2023] [Indexed: 09/05/2023]
Abstract
BACKGROUND Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer. METHODS In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method. RESULTS For all fractional models the reasonable range of fractional order is between β = 0.6 and β = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment. CONCLUSIONS At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.
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Affiliation(s)
- Shumaila Javeed
- Department of Mathematics, COMSATS University Islamabad, 45550 Islamabad, Pakistan
- Department of Computer Sciences and Mathematics, Lebanese American University, 1102-2801 Beirut, Lebanon
- Department of Mathematics, Research Centre, Near East University 99138 Nicosia / TRNC Mersin 10, Turkey
| | - Zain Ul Abdeen
- Department of Mathematics, COMSATS University Islamabad, 45550 Islamabad, Pakistan
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
- Institute of Space Sciences, R-76900 Magurele-Bucharest, Romania
- Medical University Hospital, China Medical University, 404327 Taichung, Taiwan
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Jose SA, Raja R, Dianavinnarasi J, Baleanu D, Jirawattanapanit A. Mathematical modeling of chickenpox in Phuket: Efficacy of precautionary measures and bifurcation analysis. Biomed Signal Process Control 2023. [DOI: 10.1016/j.bspc.2023.104714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/27/2023]
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Murugadoss PR, Ambalarajan V, Sivakumar V, Dhandapani PB, Baleanu D. Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays. FRONT BIOSCI-LANDMRK 2023; 28:117. [PMID: 37395028 DOI: 10.31083/j.fbl2806117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Revised: 04/26/2023] [Accepted: 05/05/2023] [Indexed: 07/04/2023]
Abstract
BACKGROUND Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. METHODS The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. RESULTS Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. CONCLUSIONS The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.
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Affiliation(s)
- Prakash Raj Murugadoss
- Department of Mathematics, A.V.V.M. Sri Pushpam College (Affiliated to Bharathidasan University, Tiruchirappalli), Poondi, 613 503 Thanjavur, Tamil Nadu, India
| | - Venkatesh Ambalarajan
- Department of Mathematics, A.V.V.M. Sri Pushpam College (Affiliated to Bharathidasan University, Tiruchirappalli), Poondi, 613 503 Thanjavur, Tamil Nadu, India
| | - Vinoth Sivakumar
- Department of Mathematics, V.S.B. Engineering College, 639111 Karur, Tamil Nadu, India
| | | | - Dumitru Baleanu
- Department of Mathematics, Cankara University, 06530 Ankara, Turkey
- Institute of Space Sciences, Laboratory of Theoretical Physics, R 76900, Magurele-Bucharest, Romania
- Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, 11022801 Beirut, Lebanon
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Chu YM, Rashid S, Akdemir AO, Khalid A, Baleanu D, Al-Sinan BR, Elzibar OAI. Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model. Results Phys 2023; 49:106467. [PMID: 37153140 PMCID: PMC10140436 DOI: 10.1016/j.rinp.2023.106467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/12/2023] [Revised: 04/13/2023] [Accepted: 04/17/2023] [Indexed: 05/09/2023]
Abstract
The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.
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Affiliation(s)
- Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, 313000, China
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
| | - Ahmet Ocak Akdemir
- Department of Mathematics, Faculty of Science and Arts, Agri Ibrahim Cecen University, Agrı, Turkey
| | - Aasma Khalid
- Department of Mathematics, Government College women University, Faisalabad, Pakistan
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, 06530 Bucharest, Romania
- Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon
| | - Bushra R Al-Sinan
- University of Hafr Al-Batin, Nairiyah College, Department of Administrative and Financial Sciences, Saudi Arabia
| | - O A I Elzibar
- Department of Mathematics, Turabah University College, Taif University, P.O. Box 1109, Taif 21944, Saudi Arabia
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Alijani Z, Shiri B, Perfilieva I, Baleanu D. Numerical solution of a new mathematical model for intravenous drug administration. Evol Intel 2023. [DOI: 10.1007/s12065-023-00840-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
Abstract
AbstractWe develop and analyze a new mathematical model for intravenous drug administration and the associated diffusion process. We use interval analysis to obtain a system of weakly singular Volterra integral equations over ordinary functions. We then use the operational method based on Chebyshev polynomials for obtaining an approximate solution of the numerical form. We show that for a certain class of fuzzy number valued functions, their generalized Hukuhara derivatives can be reduced to the derivatives of ordinary real-valued functions. By using our approach, we are able to estimate numerical solutions very accurately.
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kumari S, Singh K, Khan T, Ariffin MM, Mohan SK, Baleanu D, Ahmadian A. A Novel Approach for Continuous Authentication of Mobile Users Using Reduce Feature Elimination (RFE): A Machine Learning Approach. Mobile Netw Appl 2023. [DOI: 10.1007/s11036-023-02103-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/27/2022] [Indexed: 09/15/2023]
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13
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Naik MK, Baishya C, Veeresha P, Baleanu D. Design of a fractional-order atmospheric model via a class of ACT-like chaotic system and its sliding mode chaos control. Chaos 2023; 33:023129. [PMID: 36859205 DOI: 10.1063/5.0130403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
Investigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations.
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Affiliation(s)
- Manisha Krishna Naik
- Department of Studies and Research in Mathematics, Tumkur University, Tumkur 572103, Karnataka, India
| | - Chandrali Baishya
- Department of Studies and Research in Mathematics, Tumkur University, Tumkur 572103, Karnataka, India
| | - Pundikala Veeresha
- Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, India
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Balgat, 06530 Ankara, Turkey
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Ahmad S, Javeed S, Raza S, Baleanu D. A novel fractional model for the projection of households using wealth index quintiles. PLoS One 2022; 17:e0277472. [PMID: 36395109 PMCID: PMC9671317 DOI: 10.1371/journal.pone.0277472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 10/28/2022] [Indexed: 11/19/2022] Open
Abstract
Forecasting household assets provides a better opportunity to plan their socioeconomic activities for the future. Fractional mathematical models offer to model the asset-holding data into a piece of scientific evidence in addition to forecasting their future value. This research focuses on the development of a new fractional mathematical model based on the wealth index quintile (WIQ) data. To accomplish the objective, we used the system of coupled fractional differential equations by defining the fractional term with the Caputo derivative and verified it with the stability tests considering the steady-state solution. A numerical solution of the model was obtained using the Adams-Bashforth-Moulton method. To validate the model, we used real-time data obtained from the household series of surveys in Punjab, Pakistan. Different case studies that elucidate the effect of quintiles on the population are also presented. The accuracy of results between real-world and simulated data was compared using absolute and relative errors. The synchronization between the simulated results and real-time data verifies the formulation of the fractional WIQ model. This fractional model can be utilized to predict the approximation of the asset-holding of the households. Due to its relative nature, the model also provides the opportunity for the researchers to use the WIQs of their respective regions to forecast the households' socioeconomic conditions.
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Affiliation(s)
- Shakoor Ahmad
- Department of Mathematics, COMSATS University Islamabad, Chak Shahzad Islamabad, Pakistan
| | - Shumaila Javeed
- Department of Mathematics, COMSATS University Islamabad, Chak Shahzad Islamabad, Pakistan
- Department of Mathematics, Near East University, Mathematics Research Center, Nicosia /Mersin, Turkey
- * E-mail:
| | - Saqlain Raza
- Respiratory Care Department, College of Applied Medical Sciences in Jubail, Imam Abdulrahman bin Faisal University, Jubail, Saudi Arabia
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
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15
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Sweilam N, Al-Mekhlafi S, Shatta S, Baleanu D. Numerical treatments for the optimal control of two types variable-order COVID-19 model. Results Phys 2022; 42:105964. [PMID: 36092971 PMCID: PMC9444160 DOI: 10.1016/j.rinp.2022.105964] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Revised: 08/22/2022] [Accepted: 08/31/2022] [Indexed: 05/10/2023]
Abstract
In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.
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Affiliation(s)
- Nasser Sweilam
- Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
| | - Seham Al-Mekhlafi
- Department of Mathematics, Faculty of Education, Sana'a University, Yemen
- Department of Engineering Mathematics and Physics, Future University in Egypt, Egypt
| | - Salma Shatta
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
| | - Dumitru Baleanu
- Cankaya University, Department of Mathematics, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
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Altan G, Alkan S, Baleanu D. A novel fractional operator application for neural networks using proportional Caputo derivative. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07728-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Baleanu D, Srivastava HM, Cattani C. Editorial: Recent advances in computational biology. Chaos Solitons Fractals 2022; 163:112579. [PMID: 36061952 PMCID: PMC9417655 DOI: 10.1016/j.chaos.2022.112579] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Affiliation(s)
- Dumitru Baleanu
- Cankaya University, Department of Mahematics, Balgat, 06530 Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
| | - Hari Mohan Srivastava
- Department of Mathematics and Statistics,University of Victoria,Victoria, British Columbia V8W 3R4,Canada
| | - Carlo Cattani
- Engineering School (DEIM), University of Tuscia, Largo dell'Université, Viterbo 01100, Italy
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Razip MM, Savita KS, Kalid KS, Ahmad MN, Zaffar M, Abdul Rahim EE, Baleanu D, Ahmadian A. The development of sustainable IoT E-waste management guideline for households. Chemosphere 2022; 303:134767. [PMID: 35526685 DOI: 10.1016/j.chemosphere.2022.134767] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Revised: 04/20/2022] [Accepted: 04/25/2022] [Indexed: 06/14/2023]
Abstract
The introduction of new technology, such as the Internet of Things (IoT), entails a growth in digital devices, which could ultimately result in a high amount of electronic trash (e-waste) production if they are not appropriately managed. Apart from that, the regulation on possible "IoT E-waste" generation is yet to be regulated, probably due to the new development and implementation of IoT globally. Hence, this paper proposed a Sustainable IoT E-waste Management guideline for households. This guideline could assist government agencies and policymakers in their strategies, planning, development, and implementation of a sustainable household IoT e-waste management initiatives in Malaysia. This study is an exploratory study that adopts a qualitative case study research method. The guideline was developed based on the Integrated Sustainable Waste Management (ISWM) Model. This guideline contributes to Malaysia's sustainability agenda in reducing carbon emissions intensity towards 2030 by 45 percent.
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Affiliation(s)
- Marym Mohamad Razip
- Department of Computer and Information Sciences, Positive Computing, Universiti Teknologi PETRONAS, Perak, Malaysia
| | - K S Savita
- Department of Computer and Information Sciences, Positive Computing, Universiti Teknologi PETRONAS, Perak, Malaysia.
| | - Khairul Shafee Kalid
- Department of Computer and Information Sciences, Positive Computing, Universiti Teknologi PETRONAS, Perak, Malaysia
| | | | - Maryam Zaffar
- Faculty Of Computer Science, IBADAT International University Islamabad, Pakistan
| | | | - Dumitru Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey; Lebanese American University,11022801, Beirut, Lebanon; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
| | - Ali Ahmadian
- School of Mathematical Sciences, College of Science and Technology, Wenzhou-Kean University, Wenzhou, China; Department of Mathematics, Near East University, Nicosia, TRNC, Mersin, 10, Turkey
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Baleanu D, Arshad S, Jajarmi A, Shokat W, Ghassabzade FA, Wali M. Dynamical behaviours and stability analysis of a generalized fractional model with a real case study. J Adv Res 2022:S2090-1232(22)00191-6. [PMID: 36049735 PMCID: PMC9420693 DOI: 10.1016/j.jare.2022.08.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Revised: 07/31/2022] [Accepted: 08/14/2022] [Indexed: 11/22/2022] Open
Abstract
Introduction Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. Objectives The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. Methods The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. Results Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. Conclusion According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.
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Affiliation(s)
- D Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, 06530 Ankara, Turkey; Institute of Space Sciences, P.O.Box, MG-23, R 76900, Magurele-Bucharest, Romania; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - S Arshad
- COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
| | - A Jajarmi
- Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran.
| | - W Shokat
- COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
| | - F Akhavan Ghassabzade
- Department of Mathematics, Faculty of Sciences, University of Gonabad, Gonabad, Iran
| | - M Wali
- COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
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20
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Karaca Y, Baleanu D, Karabudak R. Hidden Markov Model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of Multiple Sclerosis’ subgroups. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.108694] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Mohammed PO, O'Regan D, Baleanu D, Hamed YS, Elattar EE. Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions. Math Biosci Eng 2022; 19:7272-7283. [PMID: 35730306 DOI: 10.3934/mbe.2022343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where $ \left({}_{{c_0}}^{C{F_R}}\nabla^{\theta} \mathtt{F}\right)(t) > -\epsilon\, \Lambda(\theta-1)\, \bigl(\nabla \mathtt{F}\bigr)(c_{0}+1) $ such that $ \bigl(\nabla \mathtt{F}\bigr)(c_{0}+1)\geq 0 $ and $ \epsilon > 0 $. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of $ \epsilon $ and $ \theta $.
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Affiliation(s)
- Pshtiwan Othman Mohammed
- Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
| | - Donal O'Regan
- School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
- Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
- China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
| | - Y S Hamed
- Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia
| | - Ehab E Elattar
- Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia
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22
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Ibrahim RW, Baleanu D. Convoluted fractional differentials of various forms utilizing the generalized Raina's function description with applications. Journal of Taibah University for Science 2022. [DOI: 10.1080/16583655.2022.2070836] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Rabha W. Ibrahim
- The Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, USA
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
- Department of Medical Research, China Medical University, Taichung, Taiwan
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23
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Liu X, Razi Othman A, H. Abu-Hamdeh N, Abusorrah AM, Karimipour A, Li Z, Ghaemi F, Baleanu D. The Molecular Dynamics study of atomic structure behavior of LL-37 peptide as the antimicrobial agent, derived from the human cathelicidin, inside a nano domain filled by the aqueous environment. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2021.118187] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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25
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Guirao JLG, Sabir Z, Raja MAZ, Baleanu D. Design of neuro-swarming computational solver for the fractional Bagley-Torvik mathematical model. Eur Phys J Plus 2022; 137:245. [PMID: 35223352 PMCID: PMC8856882 DOI: 10.1140/epjp/s13360-022-02421-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
This study is to introduce a novel design and implementation of a neuro-swarming computational numerical procedure for numerical treatment of the fractional Bagley-Torvik mathematical model (FBTMM). The optimization procedures based on the global search with particle swarm optimization (PSO) and local search via active-set approach (ASA), while Mayer wavelet kernel-based activation function used in neural network (MWNNs) modeling, i.e., MWNN-PSOASA, to solve the FBTMM. The efficiency of the proposed stochastic solver MWNN-GAASA is utilized to solve three different variants based on the fractional order of the FBTMM. For the meticulousness of the stochastic solver MWNN-PSOASA, the obtained and exact solutions are compared for each variant of the FBTMM with reasonable accuracy. For the reliability of the stochastic solver MWNN-PSOASA, the statistical investigations are provided based on the stability, robustness, accuracy and convergence metrics.
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Affiliation(s)
- Juan L. G. Guirao
- Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia
- Lab Theor Cosmology, Int Centre of Gravity and Cosmos, TUSUR, Tomsk, Russia 634050
| | - Zulqurnain Sabir
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002 Taiwan, Republic of China
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Science, Magurele-Bucharest, Romania
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26
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Mohammed PO, Goodrich CS, Brzo AB, Baleanu D, Hamed YS. New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel. Math Biosci Eng 2022; 19:4062-4074. [PMID: 35341286 DOI: 10.3934/mbe.2022186] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The $ \nu- $monotonicity definitions, namely $ \nu- $(strictly) increasing and $ \nu- $(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with $ \nu- $monotonicity definitions, we find that the investigated discrete fractional operators will be $ \nu^2- $(strictly) increasing or $ \nu^2- $(strictly) decreasing in certain domains of the time scale $ \mathbb{N}_a: = \{a, a+1, \dots\} $. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.
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Affiliation(s)
- Pshtiwan Othman Mohammed
- Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
| | | | - Aram Bahroz Brzo
- Department of Physics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest R76900, Romania
- Department of Mathematics, King Abdul Aziz University, Jeddah 21577, Saudi Arabia
| | - Yasser S Hamed
- Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
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Jayakumar C, Santra SS, Baleanu D, Edwan R, Govindan V, Murugesan A, Altanji M. Oscillation result for half-linear delay difference equations of second-order. Math Biosci Eng 2022; 19:3879-3891. [PMID: 35341278 DOI: 10.3934/mbe.2022178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.
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Affiliation(s)
- Chinnasamy Jayakumar
- Department of Mathematics, Mahendra Arts & Science College (Autonomous), Kalipatti, Namakkal Dt., Tamil Nadu, India
| | - Shyam Sundar Santra
- Department of Mathematics, JIS College of Engineering, Kalyani 741235, India
| | - Dumitru Baleanu
- Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University Ankara, 06790 Etimesgut, Turkey
- Instiute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China
| | - Reem Edwan
- College Of Science And arts, Al-Ola, Taibah University, Al madinah Al Munawwarahn 344, Saudi Arabia
| | - Vediyappan Govindan
- Department of Mathematics, Dmi St John The Baptist University, 800-Central Africa, Malawi
| | - Arumugam Murugesan
- Department of Mathematics, Government Arts College (Autonomous), Salem - 636007, Tamil Nadu, India
| | - Mohamed Altanji
- Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
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Alian Moghadam R, Mohammad Sajadi S, Abu-Hamdeh NH, Bezzina S, Kalbasi R, Karimipour A, Ghaemi F, Baleanu D. Water molecules adsorption by a porous carbon matrix in the presence of NaCl impurities using molecular dynamic simulation. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2021.117998] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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29
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Kumar P, Baleanu D, Erturk VS, Inc M, Govindaraj V. A delayed plant disease model with Caputo fractional derivatives. Adv Contin Discret Model 2022; 2022:11. [PMID: 35450199 PMCID: PMC8799979 DOI: 10.1186/s13662-022-03684-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 01/08/2022] [Indexed: 04/25/2023]
Abstract
We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.
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Affiliation(s)
- Pushpendra Kumar
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609 India
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, R76900 Romania
| | - Vedat Suat Erturk
- Department of Mathematics, Ondokuz Mayis University, Atakum, 55200 Samsun Turkey
| | - Mustafa Inc
- Department of Computer Engineering, Biruni Universiity, Istanbul, Turkey
- Department of Mathematics, Science Faculty, Firat University, Elazig, 23119 Turkey
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - V. Govindaraj
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609 India
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Abdelhakem M, Ahmed A, Baleanu D, El-kady M. Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems. Comp. Appl. Math. 2022; 41:253. [PMCID: PMC9297062 DOI: 10.1007/s40314-022-01940-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Revised: 06/02/2022] [Accepted: 06/07/2022] [Indexed: 09/02/2023]
Abstract
We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices’ efficiency and accuracy.
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Affiliation(s)
- M. Abdelhakem
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
- Basic Science Department, School of Engineering, Canadian International College (CIC), New Cairo, Egypt
| | - A. Ahmed
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
| | - D. Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
- Lebanese American University, 11022801 Beirut, Lebanon
| | - M. El-kady
- Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt
- Basic Science Department, School of Engineering, Canadian International College (CIC), New Cairo, Egypt
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Qaraad B, Moaaz O, Baleanu D, Santra SS, Ali R, Elabbasy EM. Third-order neutral differential equations of the mixed type: Oscillatory and asymptotic behavior. Math Biosci Eng 2022; 19:1649-1658. [PMID: 35135222 DOI: 10.3934/mbe.2022077] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results.
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Affiliation(s)
- B Qaraad
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
- Department of Mathematics, Faculty of Science, Amran University, Amran, Yemen
| | - O Moaaz
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
- Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, Roma 39, 00186, Italy
| | - D Baleanu
- Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Çankaya University Ankara, Etimesgut 06790, Turkey
- Instiute of Space Sciences, Magurele-Bucharest, Magurele 077125, Romania; Department of Medical Research, China
- Medical University Hospital, China Medical University, Taiwan, China
| | - S S Santra
- Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal - 741235, India
| | - R Ali
- Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
| | - E M Elabbasy
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Muhib A, Dassios I, Baleanu D, Santra SS, Moaaz O. Odd-order differential equations with deviating arguments: asymptomatic behavior and oscillation. Math Biosci Eng 2022; 19:1411-1425. [PMID: 35135210 DOI: 10.3934/mbe.2022065] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Despite the growing interest in studying the oscillatory behavior of delay differential equations of even-order, odd-order equations have received less attention. In this work, we are interested in studying the oscillatory behavior of two classes of odd-order equations with deviating arguments. We get more than one criterion to check the oscillation in different methods. Our results are an extension and complement to some results published in the literature.
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Affiliation(s)
- A Muhib
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
- Department of Mathematics, Faculty of Education - Al-Nadirah, Ibb University, Ibb, Yemen
| | - I Dassios
- AMPSAS, University College Dublin, D4 Dublin, Ireland
| | - D Baleanu
- Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Çankaya University Ankara, 06790 Etimesgut, Turkey
- Instiute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania; Department of Medical Research, China
- Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, China
| | - S S Santra
- Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal - 741235, India
| | - O Moaaz
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
- Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy
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Hou E, Hussain A, Rehman A, Baleanu D, Nadeem S, Matoog RT, Khan I, Sherif ESM. Entropy generation and induced magnetic field in pseudoplastic nanofluid flow near a stagnant point. Sci Rep 2021; 11:23736. [PMID: 34887469 PMCID: PMC8660917 DOI: 10.1038/s41598-021-02997-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Accepted: 11/22/2021] [Indexed: 12/05/2022] Open
Abstract
In this present article the entropy generation, induced magnetic field, and mixed convection stagnant point flow of pseudoplastic nano liquid over an elastic surface is investigated. The Buongiorno model is employed in modeling. Through the use of the boundary layer idea, flow equations are transformed from compact to component form. The system of equations is solved numerically. The Induced magnetic spectrum falls near the boundary and grows further away as the reciprocal of the magnetic Prandtl number improves. The fluctuation of induced magnetic rises while expanding the values of mixed convection, thermophoresis, and magnetic parameters, whereas it declines for increment in the Brownian and stretching parameters. The velocity amplitude ascends and temperature descends for the rise in magnetic parameter. The mass transfer patterns degrade for the higher amount of buoyancy ratio while it boosts by the magnification of mixed convection and stretching parameters. Streamlines behavior is also taken into account against the different amounts of mixed convection and magnetic parameters. The pseudoplastic nanofluids are applicable in all electronic devices for increasing the heating or cooling rate in them. Further, pseudoplastic nanofluids are also applicable in reducing skin friction coefficient.
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Affiliation(s)
- Enran Hou
- College of Mathematics, Huaibei Normal University, Huaibei, 235000, China
| | - Azad Hussain
- Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan
| | - Aysha Rehman
- Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan.
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, 077125, Magurele, Romania
| | - Sohail Nadeem
- Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan
| | - R T Matoog
- Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
| | - Ilyas Khan
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
| | - El-Sayed M Sherif
- Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box 800, Al-Riyadh, 11421, Saudi Arabia
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Jamshed W, Baleanu D, Nasir NAAM, Shahzad F, Nisar KS, Shoaib M, Ahmad S, Ismail KA. The improved thermal efficiency of Prandtl-Eyring hybrid nanofluid via classical Keller box technique. Sci Rep 2021; 11:23535. [PMID: 34876598 PMCID: PMC8651691 DOI: 10.1038/s41598-021-02756-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 11/22/2021] [Indexed: 11/09/2022] Open
Abstract
Prandtl-Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo-Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl-Eyring variable-II are improved.
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Affiliation(s)
- Wasim Jamshed
- Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan.
| | - Dumitru Baleanu
- Institute of Space Sciences, 077125, Magurele-Bucharest, Romania. .,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan. .,Department of Mathematics, Cankaya University, Balgat, 06530, Turkey.
| | - Nor Ain Azeany Moh Nasir
- grid.449287.40000 0004 0386 746XDepartment of Mathematics, Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Kem Sungai Besi, 57000 Kuala Lumpur, Malaysia
| | - Faisal Shahzad
- grid.509787.40000 0004 4910 5540Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000 Pakistan
| | - Kottakkaran Sooppy Nisar
- grid.449553.a0000 0004 0441 5588Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, 11991 Saudi Arabia
| | - Muhammad Shoaib
- grid.418920.60000 0004 0607 0704Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
| | - Sohail Ahmad
- grid.411501.00000 0001 0228 333XCentre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan, 60800 Pakistan
| | - Khadiga Ahmed Ismail
- grid.412895.30000 0004 0419 5255Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, Taif University, P.O. Box 11099, Taif, 21944 Saudi Arabia
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Ahmad W, Abbas M, Rafiq M, Baleanu D. Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic. Results Phys 2021; 31:104917. [PMID: 34722138 PMCID: PMC8536489 DOI: 10.1016/j.rinp.2021.104917] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Revised: 10/10/2021] [Accepted: 10/13/2021] [Indexed: 05/04/2023]
Abstract
In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.
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Affiliation(s)
- W Ahmad
- Department of Mathematics, GC University, Lahore, Pakistan
| | - M Abbas
- Department of Mathematics, GC University, Lahore, Pakistan
| | - M Rafiq
- Department of Mathematics, Faculty of Sciences, University of Central Punjab Lahore, Pakistan
| | - D Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele, Bucharest, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
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Shahzad F, Baleanu D, Jamshed W, Nisar KS, Eid MR, Safdar R, Ismail KA. Flow and heat transport phenomenon for dynamics of Jeffrey nanofluid past stretchable sheet subject to Lorentz force and dissipation effects. Sci Rep 2021; 11:22924. [PMID: 34824317 PMCID: PMC8617195 DOI: 10.1038/s41598-021-02212-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Accepted: 11/08/2021] [Indexed: 11/21/2022] Open
Abstract
Survey of literature unveils that nanofluids are more efficient for heat transport in comparison to the traditional fluids. However, the enlightenment of developed techniques for the augmentation of heat transport in nanomaterials has considerable gaps and, consequently, an extensive investigation for aforementioned models is vital. The ongoing investigation aims to study the 2-D, incompressible Jeffrey nanofluid heat transference flow due to a stretchable surface. Furthermore, the effect of dispersion of graphene nanoparticles in base liquid ethylene glycol (EG) on the performance of flow and heat transport using the Tawari-Das model in the existence of Ohmic heating (electroconductive heating) and viscous heat dissipation is contemplated. The boundary-layer PDEs are reconstituted as ODEs employing appropriate similarity transformation. Keller-Box Method (KBM) is utilized to determine the numerical findings of the problem. Graphene conducts heat greater in rate than all of the other materials and it is a good conductor of electrical energy. Graphene/EG nanofluid is employed to look out the parametric aspects of heat transport flow, drag coefficient, and heat transference rate phenomena with the aid of graphs and tables. The numerical outcomes indicate that concentration and magnetic field abate the shear stresses for the nanofluid. An increase of Graphene nanoparticle volume fraction parameter can boost the heat transport rate. The effect of Prandtl Number is to slow down the rate of heat transport as well as decelerate the temperature. Additionally, the rate of heat transportation augments on a surface under Deborah's number. Results indicate that the temperature of the graphene-EG nanofluid is greater than the convectional fluid hence graphene-EG nanofluid gets more important in the cooling process, biosensors and drug delivery than conventional fluids.
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Affiliation(s)
- Faisal Shahzad
- Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan.
| | - Dumitru Baleanu
- Institute of Space Sciences, 077125, Magurele-Bucharest, Romania. .,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan. .,Department of Mathematics, Cankaya University, 06530, Ankara, Turkey.
| | - Wasim Jamshed
- Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia
| | - Mohamed R Eid
- Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga, Al-Wadi Al-Gadid, 72511, Egypt.,Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321, Saudi Arabia
| | - Rabia Safdar
- Department of Mathematics, Lahore College for Women University, Lahore, 54000, Pakistan
| | - Khadiga Ahmed Ismail
- Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia
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Sabir Z, Raja MAZ, Baleanu D, Cengiz K, Shoaib M. Design of Gudermannian Neuroswarming to solve the singular Emden-Fowler nonlinear model numerically. Nonlinear Dyn 2021; 106:3199-3214. [PMID: 34785862 PMCID: PMC8581607 DOI: 10.1007/s11071-021-06901-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 09/08/2021] [Indexed: 06/01/2023]
Abstract
The current investigation is related to the design of novel integrated neuroswarming heuristic paradigm using Gudermannian artificial neural networks (GANNs) optimized with particle swarm optimization (PSO) aid with active-set (AS) algorithm, i.e., GANN-PSOAS, for solving the nonlinear third-order Emden-Fowler model (NTO-EFM) involving single as well as multiple singularities. The Gudermannian activation function is exploited to construct the GANNs-based differential mapping for NTO-EFMs, and these networks are arbitrary integrated to formulate the fitness function of the system. An objective function is optimized using hybrid heuristics of PSO with AS, i.e., PSOAS, for finding the weights of GANN. The correctness, effectiveness and robustness of the designed GANN-PSOAS are verified through comparison with the exact solutions on three problems of NTO-EFMs. The assessments on statistical observations demonstrate the performance on different measures for the accuracy, consistency and stability of the proposed GANN-PSOAS solver.
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Affiliation(s)
- Zulqurnain Sabir
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002 Taiwan, ROC
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Insitute of Space Science, Magurele-Bucharest, Romania
| | - Korhan Cengiz
- Department of Electrical-Electronics Engineering, Trakya University, 22030 Edirne, Turkey
| | - Muhammad Shoaib
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
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38
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Abidi A, Jokar Z, Allahyari S, Kolahi Sadigh F, Mohammad Sajadi S, Firouzi P, Baleanu D, Ghaemi F, Karimipour A. Improve thermal performance of Simulated-Body-Fluid as a solution with an ion concentration close to human blood plasma, by additive Zinc Oxide and its composites: ZnO/Carbon Nanotube and ZnO/Hydroxyapatite. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117457] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
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39
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Guo HH, Yazid Bajuri M, Alrabaiah H, Muhammad T, Mohammad Sajadi S, Ghaemi F, Baleanu D, Karimipour A. The investigation of energy management and atomic interaction between coronavirus structure in the vicinity of aqueous environment of H 2O molecules via molecular dynamics approach. J Mol Liq 2021; 341:117430. [PMID: 34483415 PMCID: PMC8408050 DOI: 10.1016/j.molliq.2021.117430] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Revised: 08/26/2021] [Accepted: 08/28/2021] [Indexed: 11/25/2022]
Abstract
The coronavirus pandemic is caused by intense acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Identifying the atomic structure of this virus can lead to the treatment of related diseases in medical cases. In the current computational study, the atomic evolution of the coronavirus in an aqueous environment using the Molecular Dynamics (MD) approach is explained. The virus behaviors by reporting the physical attributes such as total energy, temperature, potential energy, interaction energy, volume, entropy, and radius of gyration of the modeled virus are reported. The MD results indicated the atomic stability of the simulated virus significantly reduced after 25.33 ns. Furthermore, the volume of simulated virus changes from 182397 Å3 to 372589 Å3 after t = 30 ns. This result shows the atomic interaction between various atoms in coronavirus structure decreases in the vicinity of H2O molecules. Numerically, the interaction energy between virus and aqueous environment converges to −12387 eV and −251 eV values in the initial and final time steps of the MD study procedure, respectively.
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Affiliation(s)
- Hui-Hui Guo
- Zhejiang Provincial Key Laboratory of Media Biology and Pathogenic Control, Central Laboratory, The First Affiliated Hospital of Huzhou University, Huzhou 313000, Zhejiang, PR China
| | - Mohd Yazid Bajuri
- Department of Orthopaedics and Traumatology, Faculty of Medicine, Universiti Kebangsaan Malaysia(UKM), Kuala Lumpur, Malaysia
| | - Hussam Alrabaiah
- College of Engineering, Al Ain University, Al Ain, United Arab Emirates.,Department of Mathematics, College of Science, Tafila Technical University, Tafila, Jordan
| | - Taseer Muhammad
- Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
| | - S Mohammad Sajadi
- Department of Nutrition, Cihan University-Erbil, Kurdistan Region, Iraq.,Department of Phytochemistry, SRC, Soran University, KRG, Iraq
| | - Ferial Ghaemi
- Department of Chemical and Process Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia
| | - Dumitru Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey.,Institute of Space Sciences, Magurele, Romania.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - Arash Karimipour
- Department of Mechanical Engineering, Sapienza University of Rome, Rome, Italy
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Sabir Z, Raja MAZ, Umar M, Shoaib M, Baleanu D. FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-06452-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Naveed M, Baleanu D, Raza A, Rafiq M, Soori AH, Mohsin M. Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters. Adv Differ Equ 2021; 2021:468. [PMID: 34691162 PMCID: PMC8527452 DOI: 10.1186/s13662-021-03618-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2021] [Accepted: 10/03/2021] [Indexed: 06/13/2023]
Abstract
Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.
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Affiliation(s)
- Muhammad Naveed
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad, Pakistan
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, 06530 Balgat, Ankara Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - Ali Raza
- Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, 54000 Pakistan
- Department of Mathematics, National College of Business Administration and Economics, Lahore, 54660 Pakistan
| | - Muhammad Rafiq
- Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan
| | - Atif Hassan Soori
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad, Pakistan
| | - Muhammad Mohsin
- Department of Mathematics, Technische Universitat Chemnitz, Chemnitz, Germany
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42
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Ramzan M, Gul H, Malik MY, Baleanu D, Nisar KS. On hybrid nanofluid Yamada-Ota and Xue flow models in a rotating channel with modified Fourier law. Sci Rep 2021; 11:19590. [PMID: 34599224 PMCID: PMC8486883 DOI: 10.1038/s41598-021-98306-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Accepted: 08/30/2021] [Indexed: 11/09/2022] Open
Abstract
The present study analyzes the comparison of the Xue and Yamada-Ota models for a hybrid nanoliquid flow in porous media occurring amidst a rotating channel with surface catalyzed reaction. Here, the hybrid nanofluid flow is studied under the effect of Cattaneo Christov (C-C) heat flux and homogenous heterogeneous (Homo-Hetero) chemical reaction with entropy generation minimization analysis. The assumptions of the viscosity of hybrid nanomaterial fluid and variable thermal conductivity are added characteristics to the inimitability of the flow model. Two kinds of nanoparticles, namely single-wall carbon nanotubes and multi-wall carbon nanotubes with ethylene glycol (EG) as the base fluid are considered. Carbon nanotubes possess diverse applications in daily life including energy storage, drug delivery, cancer treatment, tissue generation, platelet activation, magnetic force microscopy, and microwave absorption, etc. Similarity transformations are utilized to translate the modeled problem into the coupled ordinary differential equations. This system of ordinary differential equations is addressed numerically. The graphical outcomes are scrutinized by utilizing the MATLAB software bvp4c function. The results revealed that the velocity profile decreases for the higher rotation parameter while increases for the escalated slip parameter. Furthermore, the fluid concentration and temperature are on the decline for higher surface catalyzed reaction and thermal relaxation parameters respectively.
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Affiliation(s)
- Muhammad Ramzan
- Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan.
| | - Hina Gul
- Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan
| | - M Y Malik
- Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, 06790, Turkey.,Institute of Space Sciences, 077125, Magurele, Bucharest, Romania.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia
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Li YX, Hekmatifar M, Sun YL, Alizadeh A, Aly AA, Toghraie D, Baleanu D, Sabetvand R. Evaluation the vibrational behavior of carbon nanotubes in different sizes and chiralities and argon flows at supersonic velocity using molecular dynamics simulation. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.116796] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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44
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Shi Y, allahyari S, Mohammad Sajadi S, Alazwari MA, Firouzi P, Abu-Hamdeh NH, Ghaemi F, Baleanu D, Karimipour A. The Molecular dynamics study of atomic Management and thermal behavior of Al-Water Nanofluid: A two phase unsteady simulation. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117286] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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45
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Ramzan M, Gul H, Baleanu D, Nisar KS, Malik MY. Role of Cattaneo-Christov heat flux in an MHD Micropolar dusty nanofluid flow with zero mass flux condition. Sci Rep 2021; 11:19528. [PMID: 34593927 PMCID: PMC8484442 DOI: 10.1038/s41598-021-98988-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Accepted: 09/06/2021] [Indexed: 11/19/2022] Open
Abstract
This investigation aims to look at the thermal conductivity of dusty Micropolar nanoliquid with MHD and Cattaneo–Christov heat flux flow over an elongated sheet. The novelty of the envisioned mathematical model is augmented with the added impacts of the heat source/sink, chemical reaction with slip, convective heat, and zero mass flux boundary conditions. The salient feature of the existing problem is to discuss the whole scenario with liquid and dust phases. The graphical depiction is attained for arising pertinent parameters by using bvp4c a built-in MATLAB function. It is noticed that the thermal profile and velocity field increases for greater values of liquid particle interaction parameter in the case of the dust phase. An escalation in the thermal profile of both liquid and dust phases is noticed for the magnetic parameter. The rate of mass transfer amplifies for large estimates of the Schmidt number. The thickness of the boundary layer and the fluid velocity are decreased as the velocity slip parameter is augmented. In both dust and liquid phases, the thermal boundary layer thickness is lessened for growing estimates of thermal relaxation time. The attained results are verified when compared with a published result.
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Affiliation(s)
- Muhammad Ramzan
- Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan.
| | - Hina Gul
- Department of Computer Science, Bahria University, Islamabad, 44000, Pakistan
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, 06790, Ankara, Turkey.,Institute of Space Sciences, 077125, Magurele-Bucharest, Romania.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia
| | - M Y Malik
- Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia
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Sweilam NH, Kumar D, Pinto CMA, Baleanu D. Editorial note on the special issue: ''Fractional calculus models for the dynamics of complex systems". J Adv Res 2021; 32:A1-A3. [PMID: 34484834 PMCID: PMC8408326 DOI: 10.1016/j.jare.2021.06.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022] Open
Affiliation(s)
- Nasser H Sweilam
- Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
| | - Devendra Kumar
- University of Rajasthan, Jaipur 302004, Rajasthan, India
| | - Carla M A Pinto
- School of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, Porto 4200-072, Portugal
| | - Dumitru Baleanu
- Institute of Space Sciences, Magurele-Bucharest, Romania.,Cankaya University, Etimesgut, Turkey
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Singh J, Ganbari B, Kumar D, Baleanu D. Analysis of fractional model of guava for biological pest control with memory effect. J Adv Res 2021; 32:99-108. [PMID: 34484829 PMCID: PMC8408328 DOI: 10.1016/j.jare.2020.12.004] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 11/25/2020] [Accepted: 12/05/2020] [Indexed: 12/04/2022] Open
Abstract
A fractional guava fruit model with memory effect is developed. Stability of the fractional model is discussed. Existence and uniqueness of the solution is examined. A numerical method is applied for numerical simulation. Effect of various parameters is analyzed on guava borers and natural enemies.
Introduction Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance.
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Affiliation(s)
- Jagdev Singh
- Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
| | - Behzad Ganbari
- Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran
| | - Devendra Kumar
- Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
| | - Dumitru Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4 06790, Etimesgut, Turkey.,Institute of Space Sciences, Magurele-Bucharest, Romania
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Ahmad I, Ouannas A, Shafiq M, Pham VT, Baleanu D. Finite-time stabilization of a perturbed chaotic finance model. J Adv Res 2021; 32:1-14. [PMID: 34484821 PMCID: PMC8408340 DOI: 10.1016/j.jare.2021.06.013] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 05/27/2021] [Accepted: 06/12/2021] [Indexed: 11/26/2022] Open
Abstract
This article proposes a new robust nonlinear controller that stabilizes a chaotic finance system in a finite-time without cancellation of the spacecraft's nonlinear terms, it improves the efficiency of the closed-loop. It accomplishes an oscillation-free faster convergence of the perturbed state variables to the desired steady-state. The proposed controller is insensitive to the parameter uncertainties of the nonlinear terms and exogenous disturbances. The paper performs a comparative study to verify the performance and efficiency of the proposed controller.
Introduction Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables’ trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. Objectives This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. Methods This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters’ effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Results Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. Conclusions This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin.
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Affiliation(s)
- Israr Ahmad
- Department of General Requirements, University of Technology and Applied Sciences, College of Applied Sciences, Nizwa, Oman
| | - Adel Ouannas
- Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi
| | - Muhammad Shafiq
- Department of Electrical and Computer Engineering, Sultan Qaboos University, Oman
| | - Viet-Thanh Pham
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey.,Department of Medical Research, China Medical University Hospital, & China Medical University Taichung, Taiwan.,Institute of Space Sciences, Magurele-Bucharest, Romania
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Sharma R, Sharma JB, Maheshwari R, Baleanu D. Early anomaly prediction in breast thermogram by hybrid model consisting of superpixel segmentation, sparse feature descriptors and extreme learning machine classifier. Biomed Signal Process Control 2021. [DOI: 10.1016/j.bspc.2021.103011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Kavitha V, Baleanu D, George S, Grayna J. Existence of measure pseudo-almost automorphic functions and applications to impulsive integro-differential equation. Chaos 2021; 31:093126. [PMID: 34598471 DOI: 10.1063/5.0060319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 09/07/2021] [Indexed: 06/13/2023]
Abstract
This article's main objective is to establish the measure pseudo-almost automorphic solution of an integro-differential equation with impulses. We develop the existence results based on the Banach contraction principle mapping and Krasnoselskii and Krasnoselskii-Schaefer type fixed point theorems. Finally, some examples are given to illustrate the significance of our theoretical findings.
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Affiliation(s)
- V Kavitha
- Department of Mathematics, Karunya Institute of Technology and Sciences (formerly Karunya University), Karunya Nagar, Coimbatore 641 114, Tamil Nadu, India
| | - Dumitru Baleanu
- Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey and Institute of Space Sciences, Magurele-Bucharest, Romania
| | - Soumya George
- Department of Mathematics, Karunya Institute of Technology and Sciences (formerly Karunya University), Karunya Nagar, Coimbatore 641 114, Tamil Nadu, India
| | - J Grayna
- Department of Mathematics, Karunya Institute of Technology and Sciences (formerly Karunya University), Karunya Nagar, Coimbatore 641 114, Tamil Nadu, India
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