Cauchy Problem for Fractional Ricatti‎ Differential Equations ‎Type with Alpha Order Caputo Fractional Derivatives

Ayad R. Khudair; S.A.M. Haddad; Sanaa L. Khalaf

Ayad R. Khudair Department of Mathematics, Faculty of Science, University of Basrah, Basrah, Iraq.
S.A.M. Haddad Department of Mathematics, Faculty of Science, University of Basrah, Basrah, Iraq
Sanaa L. Khalaf Department of Mathematics, Faculty of Science, University of Basrah, Basrah, Iraq

Keywords: Ricatti's differential equation, Caputo fractional derivatives, multi power series method, Cauchy problems

Abstract

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.

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