Numerical solution of Atangana–Baleanu–Caputo time-space fractional diffusion equation

Abstract

In this article, the time-space fractional diffusion equation is solved by using the fractional operator in Atangana–Baleanu–Caputo (ABC) sense based on the Mittag-Leffler function involving non-singular and non-local kernels. This study mainly develop the numerical method for time-space linear and non-linear ABC fractional diffusion equation by utilising centred difference approximation with second-order accuracy of Riesz fractional derivative in space and trapezoidal formula for fractional integral approximation for a system of ABC integral equations. Also, we examine the stability and show that the proposed scheme converges at the rate of [Formula: see text] having space mesh size h and time step size t. Numerical simulations are presented based on the presented method. We finished the article with a conclusion.

Keywords

• Fractional differential equation
• non-singular operator
• diffusion equation
• numerical approximation
• stability analysis
• convergence analysis