Analytical approximate solutions of the fractional convection–diffusion equation with nonlinear source term by He's homotopy perturbation method

Abstract

In this study, we present a framework to obtain analytical approximate solutions to the nonlinear fractional convection–diffusion equation. The fractional derivative is considered in the Caputo sense. The applications of the homotopy perturbation method were extended to derive analytical solutions in the form of a series with easily computed terms for this equation. Some examples are tested and the results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations of fractional order.