One Solution of Multi-term Fractional Differential Equations by Adomian Decomposition Method: Scientific Explanation

The Adomian decomposition method (ADM) is a well-known for analytical approximate solutions of linear or nonlinear ordinary differential equations (ODEs), Fractional Differential Equations (FDEs) , integral equations ,integral differential equations, etc. They arevery useful for application oriented problems .Numerical method is to obtain approximate solutions of fractional differential equations.Forexamples Legendre Pseudo-Spectral Method,vibrational iteration method, etc. H.Jafari andV.Gejji [5,10] have solved a system of nonlinear fractional differential equations and a multi order fractional differential equation using Adomian decomposition for nonlinear is functions of .In 2006,S.Momania and Zaid Odibatb[7] used the vibrational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order . O.A. Taiwo and O.S. Odetunde [8]applied approximation of multi-order fractional differential equations by an iterative decomposition method. M. M. Khader, talaat S. El danaf and A. S. Hendy [9],used efficient spectral collocation method for solving multi-term fractional differential equations based on the generalized laguerre polynomials .VedatSuatErturkShaher Momani B, Zaid Odibat [6] presented application of generalized differential transform method to multi-order fractional differential equations. In this paper we consider the Multi-term Fractional Differential Equations as form: