Abstract and Applied Analysis

Abstract and Applied Analysis / 2012 / Article
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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”

Received17 Nov 2012
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 [2]. Recently Liu applied the variational homotopy perturbation method for fractional initial boundary value problems [3]; 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 [3]: The classical variational iteration algorithm reads [4] which is exactly the same as that in Liu’s work [3], where the nonlinear term is expanded into He’s polynomials [5]. So what Liu used is exactly the variational iteration method using He’s polynomials, which has been widely used for solving various nonlinear problems [68].

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 [9], and the variational iteration algorithm using Adomian’s polynomials was given in [10].

Acknowledgment

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

References

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Copyright © 2012 Ji-Huan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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