Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2013 / Article
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Recent Advances on Methods and Applications of Nonlinear Differential Equations

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Letter to the Editor | Open Access

Volume 2013 |Article ID 860914 | https://doi.org/10.1155/2013/860914

Yi-Hong Wang, Lan-Lan Huang, "Comment on “An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method”", Mathematical Problems in Engineering, vol. 2013, Article ID 860914, 2 pages, 2013. https://doi.org/10.1155/2013/860914

Comment on “An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method”

Received07 Jan 2013
Revised16 Feb 2013
Accepted20 Feb 2013
Published27 Mar 2013

Abstract

The variational iteration method was applied to the time fractional telegraph equation and some variational iteration formulae were suggested in (Sevimlican, 2010). Those formulae are improved by Laplace transform from which the approximate solutions of higher accuracies can be obtained.


Sevimlican [1] considered the application of the variational iteration method [2, 3] to find approximate solutions of space and time fractional telegraph equations. The author suggested the following variational iteration formula for (5.1) in [1] However, in this comment, it is pointed out that the identification of the Lagrange multiplier from (4.1) to (4.9) can be improved.

According to the technique of determination of the Lagrange multipliers [4, 5], firstly, construct a correctional functional as

Assuming the Lagrange multiplier , take the Laplace transform to both sides of (2) where is the Laplace transform of .

Taking the variation with respect to , one can obtain Then, the Lagrange multiplier can be determined as Instead (see (4.9) in [1]).

As a result, the variational iteration formula is obtained as

The variational iteration formulae (5.10) and (5.17) are not right which also should be corrected, respectively.

Equation (5.10) in [1] should be

Equation (5.17) in [1] should be

Conclusions

As is well known, the VIM became an efficient analytical tool in nonlinear science since it was proposed and the method was often used in fractional differential equations. This study illustrates the method in fractional calculus can be improved by the Laplace tranform method with which the Lagrange mutipliers can be identified explicitly.

Recently, there are also other new applications of the variation iteration method to various nonlinear problems, that is, fuzzy equations [6, 7] and -fractional differential equations [8]. Readers are referred to the recent review article [9].

Acknowledgment

This work is financially supported by the Zhejiang Natural Science Foundation (Grant no. LQ12A01010).

References

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Copyright © 2013 Yi-Hong Wang and Lan-Lan Huang. 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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