{"title":"Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative","authors":"Khalid Zguaid, F. E. El Alaoui","doi":"10.1080/01630563.2023.2171055","DOIUrl":null,"url":null,"abstract":"Abstract In this manuscript, we consider the problem of regional boundary observability for semilinear time-fractional systems involving the Riemann-Liouville fractional derivative. Our primary goal is to focus on reconstructing the initial state in the desired subregion located on the boundary of the spatial domain. To do that, we firstly construct a link between regional boundary observability of the considered semilinear system and regional observability of its linear part. And with the help of an extension of the Hilbert uniqueness method (HUM), we recover the value of the initial state on the desired boundary subregion. We also provide a numerical simulation based on the steps of the HUM approach that shows the proposed algorithm’s efficiency and backs up our theoretical results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"420 - 437"},"PeriodicalIF":1.4000,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Functional Analysis and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/01630563.2023.2171055","RegionNum":4,"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: 2
Abstract
Abstract In this manuscript, we consider the problem of regional boundary observability for semilinear time-fractional systems involving the Riemann-Liouville fractional derivative. Our primary goal is to focus on reconstructing the initial state in the desired subregion located on the boundary of the spatial domain. To do that, we firstly construct a link between regional boundary observability of the considered semilinear system and regional observability of its linear part. And with the help of an extension of the Hilbert uniqueness method (HUM), we recover the value of the initial state on the desired boundary subregion. We also provide a numerical simulation based on the steps of the HUM approach that shows the proposed algorithm’s efficiency and backs up our theoretical results.
期刊介绍：
Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal.
Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.
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