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On the Nonlinear Perturbation K(n, m) Rosenau‐Hyman Equation: A Model of Nonlinear Scattering Wave

Author

Listed:
  • Abdon Atangana
  • Dumitru Baleanu
  • Maysaa’ Mohamed Al Qurashi
  • Xiao-Jun Yang

Abstract

We investigate a nonlinear wave phenomenon described by the perturbation K(n, m) Rosenau‐Hyman equation within the concept of derivative with fractional order. We used the Caputo fractional derivative and we proposed an iteration method in order to find a particular solution of the extended perturbation equation. We proved the stability and the convergence of the suggested method for solving the extended equation without any restriction on (m, n) and also on the perturbations terms. Using the inner product we proved the uniqueness of the special solution. By choosing randomly the fractional orders and m, we presented the numerical solutions.

Suggested Citation

  • Abdon Atangana & Dumitru Baleanu & Maysaa’ Mohamed Al Qurashi & Xiao-Jun Yang, 2015. "On the Nonlinear Perturbation K(n, m) Rosenau‐Hyman Equation: A Model of Nonlinear Scattering Wave," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:746327
    DOI: 10.1155/2015/746327
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    References listed on IDEAS

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    1. Carl M. Bender & Steven A. Orszag, 1999. "Advanced Mathematical Methods for Scientists and Engineers I," Springer Books, Springer, number 978-1-4757-3069-2, May.
    2. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    3. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    4. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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