A variational principle for fractal Klein-Gordon equation

IF 1.1 4区工程技术 Q4 THERMODYNAMICS

Thermal Science Pub Date : 2023-01-01 DOI:10.2298/tsci2303803c

Qiaoling Chen

引用次数: 0

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.

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分形Klein-Gordon方程的变分原理

本文研究了无限Cantor集和分形时空中的Klein-Gordon方程及其两种修正。建立并讨论了它们的变分公式，在实际应用中，时空不连续既需要空间分形导数，也需要时间分形导数。阐述了局部分数阶导数和二尺度分形导数的一些基本性质，并举例说明了欧拉-拉格朗日方程的推导。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Thermal Science 工程技术-热力学

CiteScore

2.70

自引率

29.40%

发文量

399

审稿时长

5 months

期刊介绍： The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.