Toward a new analytical method for solving nonlinear fractional differential equations

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

“…It can be concluded that the crucial step of the method is to identify the Lagrange multipliers in a more accurate way. In view of this point, several modified versions and new applications were suggested recently, see for example [22][23][24][25][26][27]. Consider the following often used FDE to illustrate the basic idea of the method,…”

Approximate analytical solution to a time-fractional Zakharov-Kuznetsov equation

“…In recent years, many methods have been developed for constructing approximate analytical solutions such as, the Adomian decomposition method (ADM) [1], the homotopy analysis method (HAM) [1], the homotopy perturbation method (HPM) [9], the variational iteration method (VIM) [2],the generalized Taylor polynimials [16], etc . Recently, Ghorbani [3] published a very interesting work whereby the approximate analytical solution of some fractional differential equations was given using a new method called Fractional Iteration Method (FIM). It was shown that this new method is very efficient and more simple to use than both of the Adomian decomposition method and the variational iteration method; since the first method has limitation due to complicated algorithms of calculating Adomian polynomials for nonlinear fractional problems and the second one requires the identification of the Lagrange multiplier which make its applicability sometimes more difficult.…”

“…More recently, Shateri and Ganji [4] employed (FIM) to solve a system of nonlinear fractional Hirota-Satsuma equations, they demonstrated the accuracy of (FIM) in few iterations. Motivated by the works [3] and [4], we aim to obtain approximate solutions of the following time-fractional Zakharov-Kuznetsov equation…”

A modified parametric iteration method for solving nonlinear second order BVPs

“…by a new easy-to-use algorithm proposed in this work, which is based on the parametric iteration method (PIM) [1,5]. Here a, b, α and β are the real constants and F is a nonlinear continuous operator with respect to its arguments.…”

“…GHORBANI, M. GACHPAZAN and J. SABERI-NADJAFI 501 2 The basic idea of the PIM In this section, we describe the PIM for solving the general second-order BVP of (1). Then the local convergence is discussed.…”