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The Time-Fractional Coupled-Korteweg-de-Vries Equations

Author

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  • Abdon Atangana
  • Aydin Secer

Abstract

We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).

Suggested Citation

  • Abdon Atangana & Aydin Secer, 2013. "The Time-Fractional Coupled-Korteweg-de-Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    • Handle: RePEc:hin:jnlaaa:947986
    DOI: 10.1155/2013/947986
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    Cited by:

    1. Arifeen, Shams Ul & Haq, Sirajul, 2023. "Petrov–Galerkin approximation of time-fractional coupled Korteweg–de Vries equation for propagation of long wave in shallow water," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 226-242.
    2. Owyed, Saud & Abdou, M.A. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Nekhili, Ramzi, 2020. "Numerical and approximate solutions for coupled time fractional nonlinear evolutions equations via reduced differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    4. Hussain, Manzoor & Haq, Sirajul & Ghafoor, Abdul, 2019. "Meshless spectral method for solution of time-fractional coupled KdV equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 321-334.
    5. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).

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