Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model
作者机构：Department of Mathematics Faculty of Science Cairo University Giza Egypt Department of Mathematics Faculty of Education Sana a University Sana'a Yemen Department of Mathematics Cankaya University Turkey Institute of Space Sciences Magurele-Bucharest Romania
出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)
年 卷 期：2018年第11卷第8期
页 面：393-423页
核心收录：
学科分类：0701[理学-数学] 070101[理学-基础数学]
主 题：Tuberculosis model optimal control problem Jacobi polynomials Caputo derivative generalized Euler method
摘 要：In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo s definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton s iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.
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