{"title":"Fractional boundary value problems and elastic sticky brownian motions","authors":"Mirko D’Ovidio","doi":"10.1007/s13540-024-00313-0","DOIUrl":null,"url":null,"abstract":"<p>We extend the results obtained in [14] by introducing a new class of boundary value problems involving non-local dynamic boundary conditions. We focus on the problem to find a solution to a local problem on a domain <span>\\(\\varOmega \\)</span> with non-local dynamic conditions on the boundary <span>\\(\\partial \\varOmega \\)</span>. Due to the pioneering nature of the present research, we propose here the apparently simple case of <span>\\(\\varOmega =(0, \\infty )\\)</span> with boundary <span>\\(\\{0\\}\\)</span> of zero Lebesgue measure. Our results turn out to be instructive for the general case of boundary with positive (finite) Borel measures. Moreover, in our view, we bring new light to dynamic boundary value problems and the probabilistic description of the associated models.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"50 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00313-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We extend the results obtained in [14] by introducing a new class of boundary value problems involving non-local dynamic boundary conditions. We focus on the problem to find a solution to a local problem on a domain \(\varOmega \) with non-local dynamic conditions on the boundary \(\partial \varOmega \). Due to the pioneering nature of the present research, we propose here the apparently simple case of \(\varOmega =(0, \infty )\) with boundary \(\{0\}\) of zero Lebesgue measure. Our results turn out to be instructive for the general case of boundary with positive (finite) Borel measures. Moreover, in our view, we bring new light to dynamic boundary value problems and the probabilistic description of the associated models.
期刊介绍：
Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
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