Abstract:
In this paper, we study the topological structure of a solution set to the Cauchy problem for semilinear differential inclusions of fractional order $\alpha\in(1, 2)$ 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 a upper semicontinuous multivalued operator of Caratheodory type. It is established that the set of solutions to the problem is an $R_\delta$-set.
Keywords:topological structure, $R_\delta$-set, differential inclusion, fractional derivative, family of cosine operator functions, multivalued map, condensing multioperator.
UDC:515.124.3
Presented:A. T. Fomenko Received: 28.08.2024 Revised: 11.03.2025 Accepted: 11.03.2025
