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.

In this paper, the Modification of He's variational iteration method (MVIM) is developed to solve fractional ordinary differential equations and fractional partial differential equations. It is used the free choice of initial approximation to propose the reliable Modification of He's variational iteration method. Some of the fractional differential equations are examined to illustrate the effectiveness and convenience of the method.The results show that the proposed method has accelerated convergence.

In [1], introduce a modified variational iteration method (MVIM) for a special kind of nonlinear differential equations. In this paper, we consider variational iteration method (VIM) and MVIM (introduced in [1]) to obtain exact solution to Fisher’s equation. It is shown in this paper the application of VIM to Fisher’s equation leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions. Therefore, we use MVIM for Fisher’s equation to overcome these disadvantages.

The variational iteration method (VIM) has been applied to solve many functional equations, so far. In this paper the problem of conversion of three radioactive materials has been studied. By mathematical modeling of the problem a system of ordinary differential equations has been derived. The variational iteration method is applied to obtain exact solution of this system of ordinary differential equations.

In this paper, the variational iteration method is proposed to solve the Nagumo telegraph equation as boundary value problems over the finite spatial interval x Î [0, L], and finite time t Î [0, t*]. Approximate solution is obtained for some special cases, so that denotes the validity of the variational iteration method. Also, this approximate solution is used to discuss the qualitative characteristics of the solution for specific initial data considered.

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results reveal that VIM is very effective and simple.