{"title":"A variational principle for fractal Klein-Gordon equation","authors":"Qiaoling Chen","doi":"10.2298/tsci2303803c","DOIUrl":null,"url":null,"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.","PeriodicalId":23125,"journal":{"name":"Thermal Science","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thermal Science","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.2298/tsci2303803c","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"THERMODYNAMICS","Score":null,"Total":0}
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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.
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.
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