ON A TOPOLOGICAL STRUCTURE OF A SOLUTION SET TO A CAUCHY PROBLEM FOR FRACTIONAL DIFFERENTIAL INCLUSIONS WITH A UPPER SEMICONTINUOUS RIGHT-HAND SIDE

In this paper, we study the topological structure of a solution set to the Cauchy problem for semilinear differential inclusions of fractional order α ∈ (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 Rδ-set.