Abstract and Applied Analysis

Applications of the Novel (G/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation

Muhammad Shakeel, Qazi Mahmood Ul-Hassan, and Jamshad Ahmad

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Abstract

We use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. When these free parameters are taken as particular values, the traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. Moreover, the numerical presentations of some of the solutions have been demonstrated with the aid of commercial software Maple. The recital of the method is trustworthy and useful and gives more new general exact solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 601961, 16 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048186

Digital Object Identifier
doi:10.1155/2014/601961

Mathematical Reviews number (MathSciNet)
MR3226213

Zentralblatt MATH identifier
07022700

Citation

Shakeel, Muhammad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad. Applications of the Novel ( ${G}^{\prime }/G$ )-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 601961, 16 pages. doi:10.1155/2014/601961. https://projecteuclid.org/euclid.aaa/1425048186


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