الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis is concerning with numerical studies for mathematical models of some real life problems. These models are the complex-order HIV infection with drug resistance during therapy, the fractional and variable order multiple time delay HIV/AIDS and Malaria. The concept of the fractional order time derivative in this study is based on the Caputo and Atangana-Baleanu definitions. A class of numerical methods is used to study the complex-order HIV infection with drug resistance during therapy model, the fractional and variable order multiple time delay HIV/AIDS and Malaria model. Theorems with their proofs are presented to study the stability analysis of the proposed methods. Numerical simulations and comparative studies are presented. Special attentions are given to study numerically HIV mathematical model of complex order with drug resistance during the therapy treatment is developed, where the derivative is defined in Caputo sense. Three numerical methods are presented to study numerically the complex order fractional HIV model. The proposed numerical methods are the Grünwald-Letnikov nonstandard finite difference method, the Grünwald-Letnikov standard finite difference method and the generalized Euler method. Comparative studies and numerical simulations are given to validate the theoretical results. On the other side, a novel model of fractional order nonlinear mathematical model of the co-infection of HIV/AIDS and Malaria with multi-delay is introduced. The suggested model is determined by a system of twelve fractional differential equation. The fractional derivative is defined in the Atangana-Baleanu Caputo sense. Two numerical methods are used for simulating the proposed system. The methods are the standard two-step Lagrange interpolation method and the nonstandard two-step Lagrange interpolation method. In order to validate the theoretical results, numerical simulations and comparative studies are given. Optimal control for the variable order fractional multi-delay differential model of the co-infection of HIV/AIDS and malaria is presented. Three control variables are presented in this model to minimize the number of the infected individuals with malaria, the co-infected individuals showing no symptoms of AIDS and the individuals asymptomatically infected with HIV/AIDS. Necessary conditions for the control problem are derived. The Grünwald-Letnikov nonstandard finite difference method is given for simulating the proposed optimal control system. The stability of the proposed method is proved.