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

AIMS Mathematics

article

M. Mossa Al-Sawalha¹  Rasool Shah²  Adnan Khan²  Osama Y. Ababneh³  Thongchai Botmart⁴ 

[1] Department of Mathematics, Faculty of Science, University of Ha'il;Department of Mathematics, Abdul Wali Khan University;Department of Mathematics, Faculty of Science, Zarqa University;Department of Mathematics, Faculty of Science, Khon Kaen University

关键词: Natural transform;    Adomian decomposition method;    Caputo-Fabrizio derivative;    Atangana-Baleanu-Caputo operator;    Korteweg-de Vries nonlinear system;   

DOI  :  10.3934/math.20221010

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY