Homotopy analysis method for fractional swift–hohenberg equation

Abstract

In this chapter, homotopy analysis method is used to obtain approximate analytic solution of the time-fractional Swift–Hohenberg equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error are calculated numerically and presented through graphs and tables for different particular cases. © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.