Numerical Methods to Solve Fractional Order Optimal Control Problems : Numerical Simulation of Fractional HIV Models Using Some Numerical Methods

ISBN-13: 9783330040267 / Angielski / Miękka / 2017 / 124 str.

Yousef S. Almaghrebi; Nasser Sweilam; Abdelhameed Nagy

Opis

In this book, two existing mathematical models to describe the human immunodeficiency virus (HIV) disease are studied. The adopted models are described by a system of nonlinear ordinary differential equations (ODEs). Optimal control 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 finite difference method (NSFDM), standard finite difference 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 defined in the sense of Caputo definition. The shifted Chebyshev spectral method (SCSM) is used to study the OS for the first model. Two different numerical methods are introduced to study the optimal control problems of both models. These methods are iterative optimal control method (IOCM) and the generalized Euler method (GEM).

O autorze

Yousef S. Almaghrebi was born in Sana'a, Yemen. Almaghrebi has M.Sc. degree in pur mathematics (2016), the faculty of science, Cairo university, Egypt. The master thesis is refereed in Arizona state university, USA, by professor ABBA GUMEL. B.Sc. degree in mathematical analysis (2010), the faculty of science, Albaath university, Homs, Syria.