In this paper, we investigate solution of the fractional Ricatti differential equations (FRDEs) with alpha order Caputo fractional derivatives. In fact, FRDEs are analogous of the Ricatti ordinary differential equations. The multi power series method is used to obtain a useful formula that is implemented to find an explicit solution of Cauchy problem for FRDEs without solving any integral. This formula is explicit and easy to compute by using Maple software to get explicit solution. Also, it is shown that the proposed formula can be used to solve the Cauchy problem for Ricatti ordinary differential equations
