Numerical solution of multi-dimensional time-fractional diffusion problems using an integral approach.

Abstract

This paper presents a significant scheme to drive the numerical solution of multi-dimensional diffusion problems where the fractional derivatives are taken in Caputo sense. The Mohand homotopy integral transform scheme (MHITS) is the composition of Mohand integral transform (MIT) and the homotopy perturbation scheme (HPS) which can be used to investigate the numerical solution in the form of convergence series. This approach does not require any presumptions, limitations on elements, or any other hypothesis. The primary objective of this strategy is to perform its direct implementation to the recurrence relation. This method produces results in the form of a convergent series, which accurately predicts the exact results. Graphical results and plot error distribution show an excellent agreement between MHITS results and the exact solution.