{"title":"A new lower bound for the $$\\textrm{L}^2$$ -norm of the Caputo fractional derivative","authors":"Marc Jornet","doi":"10.1007/s00013-024-02033-6","DOIUrl":null,"url":null,"abstract":"<p>We prove a novel, tight lower bound for the norm in <span>\\(\\textrm{L}^2[0,T]\\)</span> of the Caputo fractional derivative. It is based on continuous linear functionals, Peano kernels, and the Gaussian hypergeometric function.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00013-024-02033-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a novel, tight lower bound for the norm in \(\textrm{L}^2[0,T]\) of the Caputo fractional derivative. It is based on continuous linear functionals, Peano kernels, and the Gaussian hypergeometric function.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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