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

• Published in: Lobachevskii journal of mathematics Vol. 44; no. 8; pp. 3331 - 3342
• Main Authors: Kamenskii, M., Obukhovskii, V., Petrosyan, G.
• Format: Journal Article
• Language: English
• 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
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080223080243

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.