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STUDY OF NONLINEAR HIROTA–SATSUMA COUPLED KdV AND COUPLED mKdV SYSTEM WITH TIME FRACTIONAL DERIVATIVE

Author

Listed:
  • SIDDRA HABIB

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • AMREEN BATOOL

    (��School of Computer Science and Technology, Tiangong University, Tianjin, P. R. China)

  • ASAD ISLAM

    (��Department of Mechanical and Aerospace Engineering, Air University, Islamabad, Pakistan)

  • MUHAMMAD NADEEM

    (�Faculty of Science, Yibin University, Yibin 644000, P. R. China)

  • KHALED A. GEPREEL

    (�Department of Mathematics, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia∥Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt)

  • JI-HUAN HE

    (*School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China††National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, P. R. China)

Abstract

This paper demonstrates an effective and powerful technique, namely fractional He–Laplace method (FHe-LM), to study a nonlinear coupled system of equations with time fractional derivative. The FHe-LM is designed on the basis of Laplace transform to elucidate the solution of nonlinear fractional Hirota–Satsuma coupled KdV and coupled mKdV system but the series coefficients are evaluated in an iterative process with the help of homotopy perturbation method manipulating He’s polynomials. The fractional derivatives are considered in the Caputo sense. The obtained results confirm the suggested approach is extremely convenient and applicable to provide the solution of nonlinear models in the form of a convergent series, without any restriction. Also, graphical representation and the error estimate when compared with the exact solution are presented.

Suggested Citation

  • Siddra Habib & Amreen Batool & Asad Islam & Muhammad Nadeem & Khaled A. Gepreel & Ji-Huan He, 2021. "STUDY OF NONLINEAR HIROTA–SATSUMA COUPLED KdV AND COUPLED mKdV SYSTEM WITH TIME FRACTIONAL DERIVATIVE," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-14, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501085
    DOI: 10.1142/S0218348X21501085
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