THERMAL SCIENCE

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Qiaoling Chen

A VARIATIONAL PRINCIPLE FOR FRACTAL KLEIN-GORDON EQUATION

ABSTRACT
This paper studies the Klein-Gordon equation and two modifications in an infinite Cantor set and a fractal space-time. Their variational formulations are established and discussed, and the spatio-temporal discontinuity requires both spatio-fractal derivative and temporal fractal derivative for practical applications. Some basic properties of the local fractional derivative and the two-scale fractal derivative are elucidated, and the derivation of the Euler-Lagrange equation is illustrated.
KEYWORDS
variational theory, fractional calculation, two-scale fractal theory
PAPER SUBMITTED: 2021-12-20
PAPER REVISED: 2022-07-20
PAPER ACCEPTED: 2022-07-21
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303803C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [1803 - 1810]
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A variational principle for fractal Klein-Gordon equation

© 2024 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