期刊
AIMS MATHEMATICS
卷 7, 期 10, 页码 18334-18359出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20221010
关键词
Natural transform; Adomian decomposition method; Caputo-Fabrizio derivative; Atangana-Baleanu-Caputo operator; Korteweg-de Vries nonlinear system
The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries -modified Korteweg-de Vries system is obtained using a natural decomposition method in conjunction with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The results demonstrate that the natural decomposition technique is a very user-friendly and reliable method for dealing with fractional order nonlinear problems.
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.
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