{"title":"Approximate Controllability for Semilinear Fractional Stochastic Evolution Equations","authors":"Yiming Jiang, Jingchuang Ren, Yawei Wei, Jie Xue","doi":"10.1007/s12346-024-01133-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we show the approximate controllability for a class of semilinear fractional stochastic systems in abstract space with the Riemann–Liouville fractional derivative. The key of the proof is the existence of the mild solution for the proposed problem. These results are based on new properties of the operator obtained by the subordination principle, compact semigroup and Schauder fixed point theorem. Here we obtain the compactness of the solution operator by using Arzelà–Ascoli theorem. As an application, we establish the approximate controllability of the stochastic Rayleigh–Stokes problem for a generalized second grade fluid.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01133-6","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show the approximate controllability for a class of semilinear fractional stochastic systems in abstract space with the Riemann–Liouville fractional derivative. The key of the proof is the existence of the mild solution for the proposed problem. These results are based on new properties of the operator obtained by the subordination principle, compact semigroup and Schauder fixed point theorem. Here we obtain the compactness of the solution operator by using Arzelà–Ascoli theorem. As an application, we establish the approximate controllability of the stochastic Rayleigh–Stokes problem for a generalized second grade fluid.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.