A Continuous Dependence of a Solution Set for Fractional Differential Inclusions of an Order on Parameters and Initial Data

By using the fixed point theory for condensing multivalued maps, we prove the continuous dependence on parameters and initial data of a solution set of the Cauchy type problem for fractional order differential inclusions. We demonstrate the application of the averaging principle to the investigation...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 44; no. 8; pp. 3331 - 3342
Main Authors Kamenskii, M., Obukhovskii, V., Petrosyan, G.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 2023
Springer Nature B.V
Subjects
Algebra
Analysis
Fixed points (mathematics)
Geometry
Inclusions
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Parameters
Probability Theory and Stochastic Processes
Cauchy type problem
solution set
fractional differential inclusion
fixed point theory
continuous dependence
condensing multioperator
averaging principle
multivalued map
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Summary:By using the fixed point theory for condensing multivalued maps, we prove the continuous dependence on parameters and initial data of a solution set of the Cauchy type problem for fractional order differential inclusions. We demonstrate the application of the averaging principle to the investigation of the continuous dependence of the solution set on a parameter in the case when the right-hand side of the inclusion is rapidly oscillating.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223080243