Homotopy analysis method for solving a class of fractional partial differential equations

In this paper, the homotopy analysis method is applied to obtain the solution of fractional partial differential equations with spatial and temporal fractional derivatives in Riesz and Caputo senses, respectively. Some properties of Riesz fractional derivative utilized in obtaining the series solution are proved. Numerical examples demonstrate the effect of changing homotopy auxiliary parameter ℏ on the convergence of the approximate solution. Also, they illustrate the effect of the fractional derivative orders α and β on the solution behavior.

Research highlights
► HAM is applied to fractional partial differential equation with Riesz fractional derivative.
► Riesz fractional derivatives to some functions are evaluated.
► The effect of Riesz fractional derivative parameter on solution is presented.