Topological Structure of the Solution Set of a Cauchy Problem for Fractional Differential Inclusions with an Upper Semicontinuous Right-Hand Side

We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of...

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Published in:Doklady. Mathematics Vol. 111; no. 2; pp. 121 - 125
Main Author: Petrosyan, G. G.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2025
Springer Nature B.V
Subjects:
Banach spaces
Boundary value problems
Cauchy problems
Inclusions
Mathematics
Mathematics and Statistics
Neighborhoods
Operators (mathematics)
Ordinary differential equations
Topology
topological structure
set
differential inclusion
fractional derivative
condensing multioperator
family of cosine operator functions
multivalued map
ISSN:1064-5624, 1531-8362
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Abstract We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an -set.
AbstractList We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an -set.
We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an -set.
Author Petrosyan, G. G.
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Cites_doi 10.1080/00036811.2011.601454
10.1080/00036811.2016.1277583
10.1134/S1995080223080243
10.1016/0022-247X(86)90347-1
10.4064/fm-64-1-91-97
10.35634/vm220305
10.1016/j.camwa.2009.06.026
10.1134/S0001434624030088
10.1515/fca-2017-0075
10.1515/9783110293562
10.1515/9783110870893
10.1134/S00122661200110014
ContentType Journal Article
Copyright Pleiades Publishing, Ltd. 2025 ISSN 1064-5624, Doklady Mathematics, 2025, Vol. 111, No. 2, pp. 121–125. © Pleiades Publishing, Ltd., 2025.
Pleiades Publishing, Ltd. 2025.
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Keywords topological structure
set
differential inclusion
fractional derivative
condensing multioperator
family of cosine operator functions
multivalued map
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Snippet We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is...
We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order in Banach spaces. It is...
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StartPage 121
SubjectTerms Banach spaces
Boundary value problems
Cauchy problems
Inclusions
Mathematics
Mathematics and Statistics
Neighborhoods
Operators (mathematics)
Ordinary differential equations
Topology
Title Topological Structure of the Solution Set of a Cauchy Problem for Fractional Differential Inclusions with an Upper Semicontinuous Right-Hand Side
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