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Yi Tian

VARIATIONAL PRINCIPLE AND PERIODIC WAVE SOLUTIONALS FOR ELASTIC ROD EQUATION WITH FRACTAL DERIVATIVE

ABSTRACT
The present research paper will demonstrate the variational principle and periodic wave solutions of the elastic rod equation. First, we will illustrate the generalized variational principle in two examples. Secondly, we consider a fractal non-linear elastic rod equation with an unsmooth boundary. Based on two-scale fractal theory and the semi-inverse method, we successfully establish the fractal variational principle for the non-linear elastic rod equation. This is helpful for studying symmetry, finding conserved quantities, and revealing possible traveling solution structures of the equation. Finally, we investigate periodic wave solutions of the non-linear elastic rod equation
KEYWORDS
two-scale fractal theory, semi-inverse method, variational principle, fractal derivative
PAPER SUBMITTED: 2024-03-15
PAPER REVISED: 2024-07-02
PAPER ACCEPTED: 2024-07-02
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503871T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1871 - 1881]
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Variational principle and periodic wave solutionals for elastic rod equation with fractal derivative

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence