Numerical solution of a fractional order model of HIV infection of CD4+T cells.

Abstract

In this paper we consider a fractional order model of HIV infection of CD4+T cells and we transform this fractional order system of ordinary differential equations to a system of weakly singular integral equations. Afterwards we propose a Nystrom method for solving resulting system, convergence result and order of convergence is obtained by using conditions of existence and uniqueness of solution. Finally, we test performance of the method by numerical examples and for integer order system, we compare the obtained results with Runge-Kutta and Bessel collocation methods. Since most of the numerical methods are efficient only for intervals of small length, we also apply the introduced method for 100 days interval.

Keywords

• fractional order of differential equations
• hiv infection
• volterra integral equations
• weakly singular
• nystrom method.