Abstract
In this paper, a combinatory method of the Laplace transform and the Adomian decomposition method is proposed to solve fractional differential equations. In this scheme the solution takes the form of a convergent series with easily computable components. The chosen initial solution plays a major role as it must be of exponential order. Furthermore the basic theory of Laplace transform involving Riemann-Liouville derivative is also studied. Two examples are given to demonstrate the effectiveness of the present method.