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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562424601823