双复卡普托衍生:与二复数黎曼-刘维尔算子的比较研究及其应用

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
Mahesh Puri Goswami, Raj Kumar
{"title":"双复卡普托衍生:与二复数黎曼-刘维尔算子的比较研究及其应用","authors":"Mahesh Puri Goswami,&nbsp;Raj Kumar","doi":"10.1007/s40010-024-00885-9","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this article is to define the Caputo derivative of bicomplex order for the functions of a bicomplex variable, which we refer to as the Bicomplex Caputo Derivative (BCD) throughout the paper. We achieve BCD via the development of the Caputo derivative of bicomplex order for the bicomplex-valued functions of real variable and discuss some of its significant properties. We also compare BCD with the bicomplex Riemann–Liouville derivative and integral. We demonstrate the advantages of the properties of BCD by finding the derivatives of some elementary bicomplex functions. The useful applications of BCD are found in constructing bicomplex fractional Maxwell’s equations in the vacuum and source-free domains. The solutions of bicomplex fractional Maxwell’s equations are obtained by considering a bicomplex vector field, and it is proved that in this way the number of equations is reduced by half.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"94 3","pages":"345 - 358"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40010-024-00885-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications\",\"authors\":\"Mahesh Puri Goswami,&nbsp;Raj Kumar\",\"doi\":\"10.1007/s40010-024-00885-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The aim of this article is to define the Caputo derivative of bicomplex order for the functions of a bicomplex variable, which we refer to as the Bicomplex Caputo Derivative (BCD) throughout the paper. We achieve BCD via the development of the Caputo derivative of bicomplex order for the bicomplex-valued functions of real variable and discuss some of its significant properties. We also compare BCD with the bicomplex Riemann–Liouville derivative and integral. We demonstrate the advantages of the properties of BCD by finding the derivatives of some elementary bicomplex functions. The useful applications of BCD are found in constructing bicomplex fractional Maxwell’s equations in the vacuum and source-free domains. The solutions of bicomplex fractional Maxwell’s equations are obtained by considering a bicomplex vector field, and it is proved that in this way the number of equations is reduced by half.</p></div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":\"94 3\",\"pages\":\"345 - 358\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40010-024-00885-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-024-00885-9\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-024-00885-9","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

摘要

本文旨在定义二复变函数的二复变阶卡普托导数,本文通篇称之为二复变卡普托导数(BCD)。我们通过发展二复变实变函数的二复变阶卡普托导数来实现 BCD,并讨论了它的一些重要性质。我们还将 BCD 与二复数黎曼-刘维尔导数和积分进行了比较。我们通过求一些基本二复变函数的导数来证明 BCD 特性的优势。BCD 在构建真空域和无源域的双复分数麦克斯韦方程中得到了有用的应用。双复分数麦克斯韦方程组的解是通过考虑双复矢量场得到的,并证明通过这种方法可以将方程数量减少一半。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann–Liouville Operators and Applications

The aim of this article is to define the Caputo derivative of bicomplex order for the functions of a bicomplex variable, which we refer to as the Bicomplex Caputo Derivative (BCD) throughout the paper. We achieve BCD via the development of the Caputo derivative of bicomplex order for the bicomplex-valued functions of real variable and discuss some of its significant properties. We also compare BCD with the bicomplex Riemann–Liouville derivative and integral. We demonstrate the advantages of the properties of BCD by finding the derivatives of some elementary bicomplex functions. The useful applications of BCD are found in constructing bicomplex fractional Maxwell’s equations in the vacuum and source-free domains. The solutions of bicomplex fractional Maxwell’s equations are obtained by considering a bicomplex vector field, and it is proved that in this way the number of equations is reduced by half.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
2.60
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信