ABSTRACT
The study examines the using of Aboodh residual power series method and the Aboodh transform iteration method (ATIM) to analyze modified Korteweg-de Vries equation (mKdV) beside coupled Burger's equations in the framework of the Caputo operator. These sets of equations represent the non-linear wave description for various physical systems. Through APM and ATIM, the solution for the coupled Burger's equations and the mKdV equation get accurate dynamics information that will reveal the nature of their interactions. Using mathematically proven techniques and computational simulations, the developed methods' efficiency and reliability are illustrated in the complex behaviors of these nonlinear wave equations, so that we can gain deeper insights into their complex dynamics. The research is aimed at an increase of the knowledge about the fractional calculus utilization for nonlinear wave motion and it also provides analytical tools for an analysis of wave acting in different scientific and engineering areas.
ABSTRACT
In this paper, we consider the stochastic fractional Chen Lee Liu model (SFCLLM). We apply the mapping method in order to get hyperbolic, elliptic, rational and trigonometric stochastic fractional solutions. These solutions are important for understanding some fundamentally complicated phenomena. The acquired solutions will be very helpful for applications such as fiber optics and plasma physics. Finally, we show how the conformable derivative order and stochastic term affect the exact solution of the SFCLLM.
ABSTRACT
In this manuscript, the well-known stochastic Burgers' equation in under investigation numerically and analytically. The stochastic Burgers' equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.
ABSTRACT
COVID-19 has become a world wide pandemic since its first appearance at the end of the year 2019. Although some vaccines have already been announced, a new mutant version has been reported in UK. We certainly should be more careful and make further investigations to the virus spread and dynamics. This work investigates dynamics in Lotka-Volterra based Models of COVID-19. The proposed models involve fractional derivatives which provide more adequacy and realistic description of the natural phenomena arising from such models. Existence and boundedness of non-negative solution of the fractional model is proved. Local stability is also discussed based on Matignon's stability conditions. Numerical results show that the fractional parameter has effect on flattening the curves of the coexistence steady state. This interesting foundation might be used among the public health strategies to control the spread of COVID-19 and its mutated versions.
