Application of a domian decomposition method for solving fractional differential equation

In this paper we apply the Adomian decomposition method to find solution of fractional differential equation: AD y  BD y Cy(x)  0 m  , n 1  n ( n  1,2,3,...) (1.1) and m is integer number, with two different initial condition the first is         1 0 ( 1) (0) n p p p p C x y   , where C1, C2,... are constant, the second initial condition (0) ! (0) ( ) 1 0 k n k k y k x y     is the Taylor polynomial of order (n-1) for y, as an alternative method of Laplace transform.