An Analytical Study on Fractional Fokker-Planck Equation by Homotopy Analysis Transform Method (1311.2425v1)

Abstract: In this article we introduce an analytical method, namely Homotopy Analysis Transform Method (HATM) which is a combination of Homotopy Analysis Method (HAM) and Laplace Decomposition Method (LDM).This scheme is simple to apply linear and nonlinear fractional differential equations and having less computational work in comparison of other exiting methods.The most useful advantage of this method is to solve the fractional nonlinear differential equation without using Adomian polynomials and He polynomials for the computation of nonlinear terms.The proposed method has no linearization and restrictive assumptions throughout the process.Presently homotopy analysis transform method is used to solve time fractional Fokker-Planck equation and similar equations.The series solution obtained by HATM converges very fast.A good agreement between the obtained solution and some well-known results has been demonstrated