Improved Generalized Differential Transform Method for a Class of Linear Nonhomogeneous Ordinary Fractional Differential Equations

In this paper, by using the generalized Taylor's formula we improved the generalized differential transform method, which is a useful tool for getting the approximate analytic solutions of fractional differential equations. With this improvement, solutions of a class of linear nonhomogeneous ordinary fractional differential equations, which could not be solved with generalized differential transform method before, will be achieved and the solutions obtained will contain more integers and fractional exponents

Keywords: Fractional Differential Equations, Generalized Taylor's Formula, Generalized Differential Transform Method. 2000 MSC: 65L05, 26A33.