Iterative analysis of non-linear Swift–Hohenberg equations under nonsingular fractional order derivative

Abstract

In this article, we find an approximate analytical solution to the fractional order Swift–Hohenberg (FSH) equation by using a novel iterative method which is named Laplace Adomian decomposition method (LADM). By utilizing the proposed method, we study a nonlinear FSH equation involving and excluding dispersive terms. We compare the results through plots for different fractional order. After that, we study the aforesaid problem under Caputo–Fabrizio fractional order derivative (CFFOD). For the purpose of demonstrating our results, some examples are provided in the paper.