VARIATIONAL PRINCIPLES FOR FRACTAL BOUSSINESQ-LIKE B(m,n) EQUATION

Yan Wang, Khaled A. Gepreel and Yong-Ju Yang
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Yan Wang: School of Science, Tianjin University of Commerce, Tianjin 300134, P. R. China†Tianjin Yi-Sheng Offshore Engineering Co., Ltd., Tianjin, China
Khaled A. Gepreel: ��Department of Mathematics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
Yong-Ju Yang: �School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-8

Abstract: The variational theory has triggered skyrocketing interest in the solitary theory, and the semi-inverse method has laid the foundation for the search for a variational formulation for a nonlinear system. This paper gives a brief review of the last development of the fractal soliton theory and discusses the variational principle for fractal Boussinesq-like B(m,n) equation in the literature. The paper establishes a variational formulation for B(m, 1) equation to show the effectiveness of the semi-inverse method, and a general trial-Lagrange function with two free parameters is established for B(m,n) equation, the identification of the unknown parameters and the unknown function involved in the trial-Lagrange function is shown step by step. This paper opens a new path for the fractal variational theory.

Keywords: Two-Scale Fractal; Fractal Derivative; Fractal-Fractional Differential Equation; Euler–Lagrange Equation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500639

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