{"title":"Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media","authors":"Jamilu Hashim Hassan, Nasser-eddine Tatar, Banan Al-Homidan","doi":"10.1007/s13540-024-00299-9","DOIUrl":null,"url":null,"abstract":"<p>A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is proved in case of a strong fractional damping in the displacement component and a fractional frictional one in the volume fraction component. This extends an existing result from the integer-order (second-order) case to the non-integer case. In the absence of the fractional damping in the volume fraction component, it is shown a convergence to zero and a Lyapunov uniform stability.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"78 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-06-05","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/s13540-024-00299-9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is proved in case of a strong fractional damping in the displacement component and a fractional frictional one in the volume fraction component. This extends an existing result from the integer-order (second-order) case to the non-integer case. In the absence of the fractional damping in the volume fraction component, it is shown a convergence to zero and a Lyapunov uniform stability.
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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