Fractional Order Modeling the Gemini Virus in Capsicum annuum with Optimal Control

High performance computational approach to study model describing reversible two-step enzymatic reaction with time fractional derivative

Enzyme reactions have numerous applications in diverse disciplines of science like chemistry, biology and biomechanics. In this study, we examine the role and act of enzymes in chemical reactions which is considered in the frame of fractional order model. The proposed model includes system of four equations which are studied via Caputo fractional operator. The systems of non-linear equations are evaluated by a semi-analytical approach called q -homotopy analysis transform method. The uniqueness and existence of the solutions has been investigated through fixed point theorem. The solutions of the proposed model are achieved through the considered method and the obtained outcomes are in the form of series which shows rapid convergence. The solutions are computed and graphs are plotted for the obtained results using mathematica software. The achieved results by the proposed method are unique and illustrate the significant dynamics of the considered model via 3D plots and graphs. The results of this study demonstrate the importance and effectiveness of projected derivative and technique in the analysis of time dependent fractional mathematical models. This study also gives an idea to extend the applications of enzymatic reactions in drug development, bio mechanics, and chemical reactions in various cellular metabolisms. Also, enzymatic reactions have a vital role in the fields of the food industry for processing food, in biotechnology for the manufacture of biofuels, and in metabolic engineering to design metabolic pathways.

Analysis of a COVID-19 model with media coverage and limited resources

The novel coronavirus disease (COVID-19) pandemic has profoundly impacted the global economy and human health. The paper mainly proposed an improved susceptible-exposed-infected-recovered (SEIR) epidemic model with media coverage and limited medical resources to investigate the spread of COVID-19. We proved the positivity and boundedness of the solution. The existence and local asymptotically stability of equilibria were studied and a sufficient criterion was established for backward bifurcation. Further, we applied the proposed model to study the trend of COVID-19 in Shanghai, China, from March to April 2022. The results showed sensitivity analysis, bifurcation, and the effects of critical parameters in the COVID-19 model.

A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics

This study proposes a fractional-order mathematical model for malaria and COVID-19 co-infection using the Atangana-Baleanu Derivative. We explain the various stages of the diseases together in humans and mosquitoes, and we also establish the existence and uniqueness of the fractional order co-infection model solution using the fixed point theorem. We conduct the qualitative analysis along with an epidemic indicator, the basic reproduction number R0 of this model. We investigate the global stability at the disease and endemic free equilibrium of the malaria-only, COVID-19-only, and co-infection models. We run different simulations of the fractional-order co-infection model using a two-step Lagrange interpolation polynomial approximate method with the aid of the Maple software package. The results reveal that reducing the risk of malaria and COVID-19 by taking preventive measures will reduce the risk factor for getting COVID-19 after contracting malaria and will also reduce the risk factor for getting malaria after contracting COVID-19 even to the point of extinction.

Compatible extension of the (G'/G)-expansion approach for equations with conformable derivative

In this study, the compatible extensions of the (G'/G)-expansion approach and the generalized (G'/G)-expansion scheme are proposed to generate scores of radical closed-form solutions of nonlinear fractional evolution equations. The originality and improvements of the extensions are confirmed by their application to the fractional space-time paired Burgers equations. The application of the proposed extensions highlights their effectiveness by providing dissimilar solutions for assorted physical forms in nonlinear science. In order to explain some of the wave solutions geometrically, we represent them as two- and three-dimensional graphs. The results demonstrate that the techniques presented in this study are effective and straightforward ways to address a variety of equations in mathematical physics with conformable derivative.

A fractional order nonlinear model of the love story of Layla and Majnun

In this study, a fractional order mathematical model using the romantic relations of the Layla and Majnun is numerically simulated by the Levenberg-Marquardt backpropagation neural networks. The fractional order derivatives provide more realistic solutions as compared to integer order derivatives of the mathematical model based on the romantic relationship of the Layla and Majnun. The mathematical formulation of this model has four categories that are based on the system of nonlinear equations. The exactness of the stochastic scheme is observed for solving the romantic mathematical system using the comparison of attained and Adam results. The data for testing, authorization, and training is provided as 15%, 75% and 10%, along with the twelve numbers of hidden neurons. Furthermore, the reducible value of the absolute error improves the accuracy of the designed stochastic solver. To prove the reliability of scheme, the numerical measures are presented using correlations, error histograms, state transitions, and regression.

A fractional order model for Dual Variants of COVID-19 and HIV co-infection via Atangana-Baleanu derivative

In this paper, a new mathematical model for dual variants of COVID-19 and HIV co-infection is presented and analyzed. The existence and uniqueness of the solution of the proposed model have been established using the well known Banach fixed point theorem. The model is solved semi-analytically using the Laplace Adomian decomposition Method. The impact of the Atangana-Baleanu fractional derivative on the dynamics of the proposed model is studied. The work also highlights the impact of COVID-19 vaccination on the dynamics of the co-infection of both diseases. The model is fitted to real COVID-19 data from Botswana. The impact of COVID-19 variants on HIV prevalence using simulations is also assessed. Simulation for the class of individuals co-infected with HIV and the wild or Delta COVID-19 variant reveals a significant decrease, as vaccination rate is increased. The impact of fractional order on different epidemiological classes is also studied. Drawing the plot of total infected population with the wild and Delta COVID-19 variants, at different vaccination rates, it is concluded that, as vaccination rate is increased, there is a significant reduction in population infected with the wild and delta COVID-19 variants. The plot of class of individuals co-infected with HIV and the wild or Delta COVID-19 variant is more interesting; as vaccination rate is increased, the co-infected populations experience a significant decrease. Thus, stepping up vaccination against the different variants of COVID-19 could reduce co-infection cases largely, among people already infected with HIV.

On Fractional Inequalities Using Generalized Proportional Hadamard Fractional Integral Operator

The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator to establish some new fractional integral inequalities for extended Chebyshev functionals. In addition, we investigate some fractional integral inequalities for positive continuous functions by employing a generalized proportional Hadamard fractional integral operator. The findings of this study are theoretical but have the potential to help solve additional practical problems in mathematical physics, statistics, and approximation theory.