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

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  • Muhammad Shakeel
  • Qazi Mahmood Ul-Hassan
  • Jamshad Ahmad

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.

Suggested Citation

  • Muhammad Shakeel & Qazi Mahmood Ul-Hassan & Jamshad Ahmad, 2014. "Applications of the Novel (G′/G)‐Expansion Method for a Time Fractional Simplified Modified Camassa‐Holm (MCH) Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:601961
    DOI: 10.1155/2014/601961
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    References listed on IDEAS

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    1. Hasibun Naher & Farah Aini Abdullah & M. Ali Akbar, 2012. "New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp‐Function Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Hasibun Naher & Farah Aini Abdullah & M. Ali Akbar, 2012. "New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, January.
    3. H. Jafari & H. Tajadodi, 2010. "He's Variational Iteration Method for Solving Fractional Riccati Differential Equation," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-8, March.
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