Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions

Abstract

Purpose

The purpose of this paper is to apply a new modified homotopy perturbation method, which is effective to solve multi-order fractional equations with non-polynomial initial and boundary conditions.

Design/methodology/approach

The proposed algorithm is tested on multi-order fractional advection-dispersion equations. The fractional derivatives described in this paper are in the Caputo sense.

Findings

Approximate results explicitly reveal the complete reliability, efficiency and accuracy of the new modified technique.

Originality/value

It is observed that the approach may be implemented to other multi-fractional models with non-polynomial initial and boundary conditions.

Citation

Liu, Y. and Dong, L. (2015), "Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 1, pp. 57-67. https://doi.org/10.1108/HFF-06-2013-0187