Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

Abstract

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4 + T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

Vectorial Iterative Fractional Laplace Transform Method for the Analytic Solutions of Fractional Cauchy-Riemann Systems Partial Differential Equations

“…Riesz space-fractional derivative, the  -fractional diffusion equation, which is a special model for the twodimensional anomalous diffusion, is deduced from the basic continuous time random walk equations in terms of a time-and space-fractional partial differential equation with the Caputo time-fractional derivative of order 2  and the Riesz space-fractional derivative of order  [34]. Fractional derivatives were also used to describe HIV infection of T CD  4 with therapy effect [35].…”