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VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

YINGZI GUAN

https://orcid.org/0009-0008-4818-9427

School of Mathematics and Statistics, Huanghuai University, Zhumadian, P. R. China

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KHALED A. GEPREEL

Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

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, and

JI-HUAN HE

https://orcid.org/0000-0002-1636-0559

National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, P. R. China

E-mail Address: hejihuan@suda.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X24500543Cited by:0 (Source: Crossref)

Abstract

Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

Keywords:

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