An Approximate Solution of Nonlinear Fractional Differential Equation by Laplace Transform and Adomian Polynomials

摘要

In this paper, Laplace decomposition method is applied to obtain series solutions of nonlinear fractional differential equation. The fractional derivatives are described in the Caputo sense. The method is based on the application of Laplace transform to nonlinear differential equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The solution takes the form of a convergent series with easily computable terms. The Pade approximants are effectively used in the analysis to capture the essential behavior of the solution. Some numerical examples are presented to illustrate the efficiency and reliability of the method.