Solving Nonlinear Fractional Differential Equations using a Decomposition Method

Abstract

Over the last years, fractional differential equations have increased much consideration because of broad utilization in the mathematical modelling of physical problems. These are a generalization of classical integer order ordinary differential equations, are increasingly used to address the needs of problems in fluid mechanics, biology, engineering and other applications. It is not obvious that an exact solution of these problem types could be calculated. Generally, the numerical solutions can be derived. Various methods have been employed to solve fractional differential equations. As example, Laplace transform method, Fourier transforms method , Adomain decomposition method, and the new transform method [1-4]. The aim of the present paper is to use the Decomposition Method (DM), in order to provide explicit approximate solutions for further nonlinear fractional initial value problems.