In this paper, an attempt has been made to obtain the solution of a linear ordinary fractional differential equation by Generalized Differential Transform Method (GDTM), Homotopy Analysis Method (HAM), Adomian Decomposition Method (ADM) and Power Series Method (PSM). Differential equations of fractional order, as generalization of classical differential equations of integer order, are increasingly used to model problems in fluid flow, finance and other areas of applications. Fractional derivatives are considered in the Caputo sense. Using the present methods we can solve many linear and nonlinear fractional differential equations. These methods perform extremely well in terms of accuracy, efficiency and simplicity and provide an analytical solution in the form of an infinite power series with easily computable components.
Deepanjan Das, Rasajit Kumar Bera, Prasanta Sarkar. Unification of different numerical methods for the solution of linear fractional differential equation. International Journal of Academic Research and Development, Volume 3, Issue 1, 2018, Pages 227-239