The Reduced Differential Transform Method Forone Dimensional Time Fractional Cahn-Hilliard Equation

Abstract

The main purpose of this study is to develop a scheme to find analytic approximate solutions of initial value problems of one dimensional homogeneous time fractional Cahn-Hilliard equation by reduced differential transform method. The reduced differential transform method procedures for solving one dimensional homogeneous time fractional Cahn-Hilliard equationsubjected to the initial condition are newly developed and introduced.The reduced and inverse reduced differential transformed functions in one dimension for solving initial value problems of one dimensional homogeneous time fractional Cahn-Hilliard equation are defined.Some theorems and Corollaries used in one dimension for solving initial value problems of one dimensional homogeneous time fractional Cahn-Hilliard equation are defined and proved. The time fractional Cahn-Hilliard equation is obtained from the standard Cahn-Hilliard equation by replacing the integer order time derivative by a fractional derivative. The fractional derivative involved here is in sense of Caputo fractional derivatives, for its advantage that the initial conditions for fractional differential equations take the traditional form as for integer order differential equations.In order to show the reliability of the solutions, examples are constructed and 3D figures for some of the solutions are sketched.