Browsing by Author "AL-Mekhlafi, S.M."
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Article Nonstandard finite difference method for solving complex-order fractional Burgers’ equations(2020) Baleanu, Dumitru; AL-Mekhlafi, S.M.; Baleanu, Dumitru; 56389The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers’ equations. A new parameter σt is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter σt and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. © 2020Article Optimal control for variable order fractional HIV/AIDS and malaria mathematical models with multi-time delay(2020) Baleanu, Dumitru; AL-Mekhlafi, S.M.; Mohammed, Z.N.; Baleanu, Dumitru; 56389In this article, optimal control for variable order fractional multi-delay mathematical model for the co-infection of HIV/AIDS and malaria is presented. This model consists of twelve differential equations, where the variable order derivative are in the sense of Caputo. Three control variables are presented in this model to minimize the number of the co-infected individuals showing no symptoms of AIDS, the infected individuals with malaria, and the individuals asymptomatically infected with HIV/AIDS. Necessary conditions for the control problem are derived. The Grünwald-Letnikov nonstandard finite difference scheme is constructed to simulating the proposed optimal control system. The stability of the proposed scheme is proved. In order to validate the theoretical results numerical simulations and comparative studies are given. © 2020 Faculty of Engineering, Alexandria University