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Mathematical Problems in Engineering
Volume 2015, Article ID 871635, 6 pages
Research Article

Analytic Solutions of the Space-Time Fractional Combined KdV-mKdV Equation

1Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja 72511, Egypt
2Department of Mathematics, Faculty of Science, Northern Border University, Arar 91431, Saudi Arabia
3Department of Mathematics, Faculty of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received 27 May 2014; Revised 25 August 2014; Accepted 26 August 2014

Academic Editor: Zhong-Ke Gao

Copyright © 2015 Emad A.-B. Abdel-Salam and Zeid I. A. Al-Muhiameed. 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.


The fractional mapping method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional combined KdV-mKdV equation. Many types of exact analytical solutions are obtained. The solutions include generalized trigonometric and hyperbolic functions solutions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time.