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

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Abstract

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.

About the authors

G. G. Petrosyan

Voronezh State Pedagogical University

Email: garikpetrosyan@yandex.ru
Voronezh, Russia

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