The numerical solution of time fractional Kuramoto-Sivashinsky equations via homotopy analysis fractional Sumudu transform method

Abstract

In this communication, a new kind of semi-analytic technique has been applied to evaluate nonlinear time fractional Kuramuto–Sivashinsky equations. The method is hybridization of sumudu transform and homotopy analysis method. This technique has advancement over the traditional methods like perturbation, discretization because it does not require all these in problem solving domain. It initially transforms the problem in polynomial form and then applies the iteration using the combination of homotopic nature of known solution also called initial condition to unknown result. Finally,technique forms a series of convergent solutions, which approximate the problems towards exact solution. This method easily interprets the nonlinear nature of problems as well as memory property in the sense of time fractional derivative.