{"title":"Fractional Powers of the Quaternionic d-Bar Derivative","authors":"Arran Fernandez, Cihan Güder, Walaa Yasin","doi":"10.1007/s00006-023-01306-7","DOIUrl":null,"url":null,"abstract":"<div><p>This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from <i>n</i>th-order d-bar derivatives for <span>\\(n\\in {\\mathbb {N}}\\)</span>, and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"34 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01306-7","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from nth-order d-bar derivatives for \(n\in {\mathbb {N}}\), and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.
期刊介绍:
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.