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## Advances in Nonlinear Complexity Analysis for Partial Differential Equations

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Letter to the Editor | Open Access

Volume 2012 |Article ID 964974 | 2 pages | https://doi.org/10.1155/2012/964974

# Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”

Accepted01 Dec 2012
Published06 Dec 2012

#### Abstract

Recently Liu applied the variational homotopy perturbation method for fractional initial boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.

#### 1. Introduction

The variational iteration method [1, 2] has been shown to solve a large class of nonlinear differential problems effectively, easily, and accurately with the approximations converging rapidly to accurate solutions. In 1998, the method was first adopted to solve fractional differential equations . Recently Liu applied the variational homotopy perturbation method for fractional initial boundary value problems ; however, the method is nothing but a modified variational iteration method.

#### 2. Liu’s Work

Liu used the following example to elucidate the solution process : The classical variational iteration algorithm reads  which is exactly the same as that in Liu’s work , where the nonlinear term is expanded into He’s polynomials . So what Liu used is exactly the variational iteration method using He’s polynomials, which has been widely used for solving various nonlinear problems .

#### 3. Conclusion

The so-called variational homotopy perturbation method is nothing but the variational iteration method using He’s polynomials. A standard variational iteration algorithm using He’s polynomials is suggested to follow Guo and Mei’s work , and the variational iteration algorithm using Adomian’s polynomials was given in .

#### Acknowledgment

The work is supported by PAPD (a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions).

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