On the convergence of a new reliable algorithm for solving multi-order fractional differential equations

• We introduce a new algorithm for solving multi-order fractional differential equations.
• A comparison between the presented method with some other well-known methods for solving M-FDEs is provided.
• We present an elegant way to show the convergence analysis of the RVIM.

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods.