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Numerical techniques for solving some types of fractional order optimal control problems / Yousef Saleh Mohammed Almaghrebi ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Abdelhameed M. Nagy

By: Contributor(s): Material type: TextTextLanguage: English Publication details: Cairo : Yousef Saleh Mohammed Almaghrebi , 2016Description: 87 P. : charts ; 25cmOther title:
  • تقنيات عددية حلل بعض أنواع مسائل التحكم األمثل ذات الرتب الكسرية [Added title page title]
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Dissertation note: Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics Summary: 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).
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Thesis Thesis قاعة الرسائل الجامعية - الدور الاول المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2016.Yo.N (Browse shelf(Opens below)) Not for loan 01010110069672000
CD - Rom CD - Rom مخـــزن الرســائل الجـــامعية - البدروم المكتبة المركزبة الجديدة - جامعة القاهرة Cai01.12.17.M.Sc.2016.Yo.N (Browse shelf(Opens below)) 69672.CD Not for loan 01020110069672000

Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics

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).

Issued also as CD

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