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

Siddra Habib, Amreen Batool, Asad Islam, Muhammad Nadeem, Khaled A. Gepreel and Ji-Huan He
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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
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

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-14

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.

Keywords: FHe-LM; Fractional Derivative; Coupled KdV System; He’s Polynomials (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501085

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