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Traveling Wave Solutions of Space‐Time Fractional Generalized Fifth‐Order KdV Equation

Author

Listed:
  • Dianchen Lu
  • Chen Yue
  • Muhammad Arshad

Abstract

The Korteweg‐de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one‐dimensional nonlinear lattice. In this article, the generalized exp⁡(−Φ(ξ))‐expansion method is proposed to construct exact solutions of space‐time fractional generalized fifth‐order KdV equation with Jumarie’s modified Riemann‐Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.

Suggested Citation

  • Dianchen Lu & Chen Yue & Muhammad Arshad, 2017. "Traveling Wave Solutions of Space‐Time Fractional Generalized Fifth‐Order KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:6743276
    DOI: 10.1155/2017/6743276
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    References listed on IDEAS

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    1. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    2. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Gang wei Wang & Tian zhou Xu & Tao Feng, 2014. "Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-6, February.
    4. Sahoo, S. & Saha Ray, S., 2016. "Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G′/G)-expansion method and improved (G′/G)-expansion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 265-282.
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