Numerical approximation of the fractional HIV model using the meshless local Petrov–Galerkin method

Abstract

Abstract This paper deals with the model of fractional HIV-1 infection of CD4+T cells transformation with homogeneous Neumann boundary conditions. Numerical methods for solving fractional time differential equations are developed with Caputo’s definition. The forward difference methods were constructed applied to the approximation of the fractional time differential equation. The MLPG method is used to solve the problem of fractional HIV models for spatial discretization. Approximated solutions at the time level n use conventional iterative methods such as fixed point iterations to handle the nonlinear parts. An analysis of stability and convergence of numerical schemes is presented along with the eigenvalue of the matrix. The abilities of the developed formula was confirmed through four numerical examples base on convergence and accuracy of numerical results. The results of the numerical experiments were compared with the solution of the integer order differential equation to confirm the accuracy and efficiency of the proposed scheme. The simulation results show that the formula is easy to use and useful for those interested in fractional derivatives.

Keywords

• Caputo fractional derivative
• Fractional order differential equation
• HIV model
• Meshless local Petrov–Galerkin method