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Entropy 2015, 17(9), 6519-6533; doi:10.3390/e17096519

Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method

Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
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Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Received: 11 August 2015 / Revised: 12 September 2015 / Accepted: 18 September 2015 / Published: 23 September 2015
(This article belongs to the Special Issue Complex and Fractional Dynamics)
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Abstract

In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is comparing the results with those of the Adomian decomposition method (ADM), the variational iteration method (VIM) and the optimal homotopy asymptotic method (OHAM). Illustrative examples reveal that the present technique outperforms the aforementioned methods and can be used as an alternative for solving fractional equations. View Full-Text
Keywords: fractional power series; fractional Whitham–Broer–Kaup equations; residual power series method fractional power series; fractional Whitham–Broer–Kaup equations; residual power series method
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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. (CC BY 4.0).

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Wang, L.; Chen, X. Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method. Entropy 2015, 17, 6519-6533.

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