A New Modification of the Reconstruction of Variational Iteration Method for Solving Multi-order Fractional Differential Equations

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional differential equations (FDEs). The fractional derivatives are described in the Caputo sense. In this work, the Reconstruction of Variational Iteration Method (RVIM) technique has been successfully used to solve two types of multi-order fractional differential equations, linear and nonlinear. For this purpose, we convert FDE in to a counterpart system and then using proposed method to solve the result system. Advantage of the RVIM, is simplicity of the computations and convergent successive approximations without any restrictive assumptions. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.