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

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.