Numerical solution of fractional model of HIV infection in cells CD4+T

Subject Areas : Statistics

Mohammad Reza Doostar ¹ ( Islamic Azad University shahr-e Rey Beranch, tehran, iran )
Tayebeh Damercheli ² ( Islamic Azad University shahr-e Rey Beranch, tehran, iran )
Alireza Vahidi ³ ( Islamic Azad University shahr-e Rey Beranch, tehran, iran )

Received: 2021-05-04 Accepted : 2021-08-14 Published : 2021-09-23

Keywords: دستگاه معادلات دیفرانسیل, ماتریس عملیاتی, توابع بلاک-پالس, مشتق کسری, چندجملهایهای لژاندر,

Abstract :

In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported.

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