A Study of Continuous Dependence and Symmetric Properties of Double Diffusive Convection: Forchheimer Model

New Conditions for Testing the Oscillation of Third-Order Differential Equations with Distributed Arguments

In this paper, we consider a certain class of third-order nonlinear delay differential equations with distributed arguments. By the principle of comparison, we obtain the conditions for the nonexistence of positive decreasing solutions as well as, and by using the Riccati transformation technique, we obtain the conditions for the nonexistence of increasing solutions. Therefore, we get new sufficient criteria that ensure that every solution of the studied equation oscillates. Asymmetry plays an important role in describing the properties of solutions of differential equations. An example is given to illustrate the importance of our results.

Third-Order Neutral Differential Equations with Damping and Distributed Delay: New Asymptotic Properties of Solutions

In this paper, we are interested in studying the oscillation of differential equations with a damping term and distributed delay. We establish new criteria that guarantee the oscillation of the third-order differential equation in terms of oscillation of the second-order linear differential equation without a damping term. By using the Riccati transformation technique and the principle of comparison, we obtain new results on the oscillation for the studied equation. The results show significant improvement and extend the previous works. Symmetry contributes to determining the correct methods for solving neutral differential equations. Some examples are provided to show the significance of our results.

Comparison of Predator-Prey Model and Hawk-Dove Game for Modelling Leukemia

Game theory is an excellent mathematical tool to describe the interaction between the immune system and cancerous leukocytes (c.leu). The feature of cancerous leukocytes to differentiate and mutate to give rise to leukemia is in the domain of ecological models as well. In this work, the dynamic of leukemia is described and compared by two models: firstly by a simple probabilistic mathematical model using the zero-sum two player game of Hawk and Dove, and secondly by Leslie Predator Prey model of ecology. The main goal of this study is to compare the results of both models and then discuss the treatment of leukemia i.e., Hematopoietic Stem cell transplant with the best model among them. Hawk and Dove model also describes the cell to cell interaction of cancerous leukocytes and healthy leukocytes (leu) after diagnoses and the condition of the patient before and after treatments. In this work, Hematopoietic Stem cell transplant is discussed by using concepts of a zero-sum three player game. Also, both models will be characterized by determining the stability properties, identifying basins of attraction, and locating the equilibrium points to see, at what extent the patient's survival is possible with leukemia in its body. Results for both models will be presented graphically.

New Efficient Computations with Symmetrical and Dynamic Analysis for Solving Higher-Order Fractional Partial Differential Equations

Due to the rapid development of theoretical and computational techniques in the recent years, the role of nonlinearity in dynamical systems has attracted increasing interest and has been intensely investigated. A study of nonlinear waves in shallow water is presented in this paper. The classic form of the Korteweg–de Vries (KdV) equation is based on oceanography theory, shallow water waves in the sea, and internal ion-acoustic waves in plasma. A shallow fluid assumption is shown in the framework by a sequence of nonlinear fractional partial differential equations. Indeed, the primary purpose of this study is to use a semi-analytical technique based on Fractional Taylor Series to achieve numerical results for nonlinear fifth-order KdV models of non-integer order. Caputo is the operator used for dealing with fractional derivatives. The generated solutions of nonlinear fifth-order KdV models of non-integer order for modeling turbulence processes in the field of ocean engineering are compared analytically and numerically, to demonstrate the behaviors of several parameters of the current model. We verified the method’s convergence analysis and provided an error estimate by showing 2D and 3D graphs to further confirm its efficacy.

Analytical Solutions Formulated in the Time Domain for Three-Dimensional Heat Diffusion Equation

Two different strategies are provided to generate solutions to the three-dimensional heat diffusion equation. The first strategy is inspired by the well-known one-dimensional heat polynomial, which consists of an infinite set of polynomials, which are solutions to the one-dimensional heat diffusion equation. The second strategy is based on an exponential type function. None of the solutions presented here can be obtained by the method of separation of variables. The mathematical developments proving that, indeed, the particular solutions generated with both strategies satisfy the three-dimensional heat diffusion equation are presented. The analytical solutions are validated by generating the corresponding numerical solutions with the method of finite differences. When comparing both analytical and numerical solutions, it is found that they are identical. In addition, as part of the results, it is found that there are exponential solutions that reproduce the behavior of polynomial solutions. Finally, an example of the use of heat polynomials in engineering applications is provided.

Does freelancing have a future? Mathematical analysis and modeling

During the past few years, freelancing has grown exponentially due to the pandemic and subsequent economical changes in the world. In fact, in the last ten years, a drastic increase in freelancing has been observed; people quit their jobs to be their own boss. There are various reasons for this: downsizing of employees, not having fun in their jobs, unemployment, part time work to earn more, etc. Observing this vast change, many individuals on Facebook/YouTube, NGOs, and government departments started teaching freelancing as a course; to date, thousands of youngsters have been trained to start their careers as freelancers. It has been observed that the ratio of informed freelancers is more successful than those who start their careers independently. We construct a compartmental model to explore the influence of information on the expansion of freelancing in this article, which was motivated by this surge in freelancing. Following that, the model is subjected to dynamical analysis utilizing dynamical systems and differential equation theory. To validate our analytical conclusions, we used numerical simulation.