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New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation

Author

Listed:
  • Abdon Atangana
  • Necdet Bildik
  • S. C. Oukouomi Noutchie

Abstract

We put side by side the methodology of two comparatively new analytical techniques to get to the bottom of the system of nonlinear fractional modified Kawahara equation. The technique is described and exemplified with a numerical example. The dependability of both methods and the lessening in computations give these methods a wider applicability. In addition, the computations implicated are very simple and undemanding.

Suggested Citation

  • Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:740248
    DOI: 10.1155/2014/740248
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    3. E. Hesameddini & A. Rahimi, 2013. "A Novel Iterative Method for Solving Systems of Fractional Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, July.
    4. E. Hesameddini & A. Rahimi, 2013. "A Novel Iterative Method for Solving Systems of Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    6. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    7. Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat‐Like Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
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    Cited by:

    1. Daniel Olvera & Alex Elías-Zúñiga, 2014. "Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Nattakorn Sukantamala & Supawan Nanta, 2021. "On Solitary Wave Solutions for the Camassa‐Holm and the Rosenau‐RLW‐Kawahara Equations with the Dual‐Power Law Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    3. Chang, Chih-Wen, 2025. "Meshless scheme for solving backward higher-order time-fractional parabolic equations with an extremely long time span," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).

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