梅林变换框架内的分数贝塞尔导数

IF 1.4 4区物理与天体物理 Q2 MATHEMATICS, APPLIED

Journal of Nonlinear Mathematical Physics Pub Date : 2024-01-31 DOI:10.1007/s44198-024-00170-8

Fethi Bouzeffour

{"title":"梅林变换框架内的分数贝塞尔导数","authors":"Fethi Bouzeffour","doi":"10.1007/s44198-024-00170-8","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the work of Pagnini and Runfola, we develop a new approach by employing Tato’s type lemma for the Hankel transform. As an application, we establish a new intertwining relation between the fractional Bessel operator and the fractional second derivative, emphasizing the important role of the Mellin transform in the domain of fractional calculus associated with the Bessel operator.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"14 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional Bessel Derivative Within the Mellin Transform Framework\",\"authors\":\"Fethi Bouzeffour\",\"doi\":\"10.1007/s44198-024-00170-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the work of Pagnini and Runfola, we develop a new approach by employing Tato’s type lemma for the Hankel transform. As an application, we establish a new intertwining relation between the fractional Bessel operator and the fractional second derivative, emphasizing the important role of the Mellin transform in the domain of fractional calculus associated with the Bessel operator.</p>\",\"PeriodicalId\":48904,\"journal\":{\"name\":\"Journal of Nonlinear Mathematical Physics\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s44198-024-00170-8\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00170-8","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们利用梅林变换提出了贝塞尔算子分数幂的全新视角。我们从帕格尼尼（Pagnini）和伦福拉（Runfola）的研究中汲取灵感，利用汉克尔变换的塔托类型 Lemma，开发出一种新方法。作为应用，我们在分数贝塞尔算子和分数二阶导数之间建立了新的交织关系，强调了梅林变换在与贝塞尔算子相关的分数微积分领域中的重要作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fractional Bessel Derivative Within the Mellin Transform Framework

In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the work of Pagnini and Runfola, we develop a new approach by employing Tato’s type lemma for the Hankel transform. As an application, we establish a new intertwining relation between the fractional Bessel operator and the fractional second derivative, emphasizing the important role of the Mellin transform in the domain of fractional calculus associated with the Bessel operator.

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

Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics