Solution of variable order fractional differential equations using Homotopy Analysis Method

TL;DR

This paper applies the Homotopy Analysis Method to solve variable order fractional diffusion equations, demonstrating its effectiveness and reliability through numerical simulations for equations with spatial, temporal, or parameter-dependent orders.

Contribution

It introduces the use of Homotopy Analysis Method for variable order fractional diffusion equations, a novel approach for this class of problems.

Findings

The method effectively solves equations with space- or time-dependent fractional orders.

Numerical results confirm the reliability of the Homotopy Analysis Method for these equations.

The approach is applicable to physically important variable order fractional diffusion problems.

Abstract

In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two types of variable order fractional diffusion equations having physical importance. Numerical simulation results show that the method is reliable and effective for solving fractional order diffusion equations even when the order of the derivative is varying with respect to space or time or both or it is dependent upon some other parameters.