Yousef Saleh Mohammed Almaghrebi <br/><br/>
Numerical techniques for solving some types of fractional order optimal control problems /  
 تقنيات عددية حلل بعض أنواع مسائل التحكم األمثل ذات الرتب الكسرية  
Yousef Saleh Mohammed Almaghrebi ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Abdelhameed M. Nagy 
 - Cairo :   Yousef Saleh Mohammed Almaghrebi ,   2016 
 - 87 P. :   charts ;   25cm 
<br/><br/>Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics 
<br/><br/> In this thesis, two existing mathematical models to describe the human immun- ode ciency virus (HIV) disease are studied. The adopted models are described by a system of nonlinear ordinary di erential equations (ODEs). Optimal con- trol for HIV models is presented. The Pontryagin's Maximum Principle (PMP) is used to derive the optimality system (OS) which is solved numerically using the nonstandard  nite di erence method (NSFDM), standard  nite di erence method (SFDM) and forward-backward sweep method (FBSM). Existences and uniqueness for the solutions of the mathematical models are proved. Also, two general HIV models are presented as fractional-order mathematical models. The fractional derivative is de ned in the sense of Caputo de nition. The shifted Chebyshev spectral method (SCSM) is used to study the OS for the  rst model. Two di erent numerical methods are introduced to study the op- timal control problems of both models. These methods are iterative optimal control method (IOCM) and the generalized Euler method (GEM).  
<br/><br/>
<br/><br/><label>Subjects--Index Terms: </label>Fractional calculus   Mathematical model of HIV Optimal Control theory