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ON A TOPOLOGICAL STRUCTURE OF A SOLUTION SET TO A CAUCHY PROBLEM FOR FRACTIONAL DIFFERENTIAL INCLUSIONS WITH A UPPER SEMICONTINUOUS RIGHT-HAND SIDE
- Authors: Petrosyan G.G.1
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Affiliations:
- Voronezh State Pedagogical University
- Issue: Vol 522, No 1 (2025)
- Pages: 33-39
- Section: MATHEMATICS
- URL: https://journal-vniispk.ru/2686-9543/article/view/296216
- DOI: https://doi.org/10.31857/S2686954325020064
- EDN: https://elibrary.ru/HZAENQ
- ID: 296216
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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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