{"title":"On Impulsive Fractional Differential Inclusions with a Nonconvex-valued Multimap in Banach Spaces","authors":"V. Obukhovskii, G. Petrosyan, M. Soroka","doi":"10.1134/s1995080224601231","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study the Cauchy problem for an impulsive semilinear fractional order differential inclusion with a nonconvex-valued almost lower semicontinuous nonlinearity and a linear closed operator generating a <span>\\(C_{0}\\)</span>-semigroup in a separable Banach space. By using the fixed point theory for condensing maps, we present a global theorem on the existence of a mild solution to this problem.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224601231","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the Cauchy problem for an impulsive semilinear fractional order differential inclusion with a nonconvex-valued almost lower semicontinuous nonlinearity and a linear closed operator generating a \(C_{0}\)-semigroup in a separable Banach space. By using the fixed point theory for condensing maps, we present a global theorem on the existence of a mild solution to this problem.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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