Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives-Reference-Cited by-同舟云学术

Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives

Published:2022 Issue:10 Volume:7 Page:18334-18359
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Al-Sawalha M. Mossa¹,Shah Rasool²,Khan Adnan²,Ababneh Osama Y.³,Botmart Thongchai⁴

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 2440, Saudi Arabia

2. Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan

3. Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

4. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

<abstract><p>The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Korteweg-de Vries system is obtained in this study by employing a natural decomposition method in association with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The Korteweg-de Vries equation is considered a classical super-extension in this system. This nonlinear model scheme is commonly used to describe waves in traffic flow, electromagnetism, electrodynamics, elastic media, multi-component plasmas, shallow water waves and other phenomena. The acquired results are compared to exact solutions to demonstrate the suggested method's effectiveness and reliability. Graphs and tables are used to display the numerical results. The results show that the natural decomposition technique is a very user-friendly and reliable method for dealing with fractional order nonlinear problems.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference31 articles.

1. M. Caputo, Linear models of dissipation whose $Q$ is almost frequency independent–II, Geophys. J. Int., 13 (1967), 529–539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x

2. K. B. Oldham, J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Academic Press, 1974.

3. R. Gorenflo, F. Mainardi, Fractional calculus, In: Fractals and fractional calculus in continuum mechanics, Vienna: Springer, 1997,223–276. https://doi.org/10.1007/978-3-7091-2664-6_5

4. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Gordon and Breach Science Publishers, 1993.

5. E. Ahmed, A. M. A. El-Sayed, H. A. A. El-Saka, Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models, J. Math. Anal. Appl., 325 (2007), 542–553. https://doi.org/10.1016/j.jmaa.2006.01.087

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