{"title":"Spatial $$\\beta $$ -fractional output stabilization of bilinear systems with a time $$\\alpha $$ -fractional-order","authors":"Mustapha Benoudi, Rachid Larhrissi","doi":"10.1007/s13540-024-00354-5","DOIUrl":null,"url":null,"abstract":"<p>This research aims to investigate the stabilization problem of the Riemann-Liouville spatial <span>\\(\\beta \\)</span>-fractional output with order <span>\\(\\beta \\in (0,\\ 1)\\)</span> for a class of bilinear dynamical systems with a time Caputo <span>\\(\\alpha \\)</span>-fractional derivative. Initially, we provide definitions and establish the well-posedness of the problem addressed. Furthermore, we introduce a feedback control strategy that ensures both weak and strong stabilization of the <span>\\(\\beta \\)</span>-fractional output, under a broad set of sufficient conditions. Additionally, we present numerical computations to elucidate the effectiveness of the obtained results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"43 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-11-15","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/s13540-024-00354-5","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
This research aims to investigate the stabilization problem of the Riemann-Liouville spatial \(\beta \)-fractional output with order \(\beta \in (0,\ 1)\) for a class of bilinear dynamical systems with a time Caputo \(\alpha \)-fractional derivative. Initially, we provide definitions and establish the well-posedness of the problem addressed. Furthermore, we introduce a feedback control strategy that ensures both weak and strong stabilization of the \(\beta \)-fractional output, under a broad set of sufficient conditions. Additionally, we present numerical computations to elucidate the effectiveness of the obtained results.
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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