Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation

BAO Si-yuan; DENG Zi-chen

doi:10.3879/j.issn.1000-0887.2013.12.002

Volume 34 Issue 12

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BAO Si-yuan, DENG Zi-chen. Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1236-1246. doi: 10.3879/j.issn.1000-0887.2013.12.002

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Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation

doi: 10.3879/j.issn.1000-0887.2013.12.002

BAO Si-yuan¹,
DENG Zi-chen^2,3

¹Department of Engineering Mechanics, School of Civil Engineering,Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China;²Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;³State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Funds: The National Natural Science Foundation of China(11202146)

Received Date: 2013-08-27
Rev Recd Date: 2013-10-30
Publish Date: 2013-12-16

Abstract

Abstract

The solutions to the fractional FornbergWhitham (FFW) equation and the modified FFW equation generated by change of one nonlinear term uu_x with u²u_x were presented. The fractional variational iteration method (FVIM) was used, in which the Lagrange multiplier was determined with the variational function and the Laplace transformation. Two cases were discussed respectively for the FFW equation because the order of time differentiation was determined through comparison of the two derivatives’orders in the fractional differential equation. Finally, two numerical examples of the FVIM solution were given. The computational results demonstrate the high efficiency of the presented method.
- fractional FornbergWhitham equation,
- fractional variational iteration method,
- Lagrange multiplier,
- approximate solution,
- initial value problem

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References

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