ANALYTICAL APPROXIMATE SOLUTION FOR NONLINEAR SPACE-TIME FRACTIONAL CAHN-HILLIARD EQUATION

Abstract

The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Cahn-Hilliard equation. The numerical results show that the approaches are easy to implement and accurate when applied to the non- linear space-time fractional derivatives Cahn-Hilliard equation. This method intro- duces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equat. The HAM contains a certain auxiliary parameter h which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution.