On the Numerical Method for Solving a System of Nonlinear Fractional Ordinary Differential Equations Arising in HIV Infection of CD4~+ T Cells

摘要

In this study, shifted Legendre collocation method is used to provide an approximate solution of a fractional order model of HIV infection of CD4+ T cells. This model corresponds to a nonlinear system of fractional ordinary differential equation. By using the present method, the solution of this nonlinear system converts to the solution of nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton's method. Furthermore, convergence and error analysis of the proposed method are discussed and an upper error bound is provided under weak assumptions. Finally, numerical results for solving fractional model of HIV infection of CD4+ T cells with various parameters are reported in tables. Also, we survey the effect of changing the parameter on the present model.