Solving Fractional Ordinary Differential Equations Using FNDM

Mahmoud Saleh Rawashdeh

Abstract

Our goal of the present paper is to propose new and easy method called the
Fractional Natural Decomposition Method (FNDM). The FNDM is a combination of the Natural transform method (NTM) and the Adomian decomposition method (ADM). We use the FNDM to construct analytic approximate and exact solutions to some applications of Fractional Ordinary Differential Equation (FODEs), namely; the fractional nonhomogeneous Bagley--Torvik equation, the composite fractional oscillation equation and three other fractional ordinary differential equations. The fractional derivatives are described in the Caputo sense. One can conclude the new method is easy and efficient.