On the averaging principle for semilinear fractional differential inclusions in a banach space with a deviating argument and a small parameter
- Authors: Kamenskii M.I.1, Petrosyan G.G.2
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Affiliations:
- Воронежский государственный университет
- Воронежский государственный университет инженерных технологий
- Issue: Vol 204 (2022)
- Pages: 74-84
- Section: Статьи
- URL: https://journal-vniispk.ru/2782-4438/article/view/269987
- DOI: https://doi.org/10.36535/0233-6723-2022-204-74-84
- ID: 269987
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Abstract
The this paper, we considers the Cauchy problem for a class of semilinear differential inclusions in a separable Banach space involving a fractional Caputo derivative of order q ∈ (0,1), a small parameter, and a deviant argument. We assume that the linear part of the inclusion generates a Со-semigroup. In the space of continuous functions, we construct a multivalued integral operator whose fixed points are solutions. An analysis of the dependence of this operator on a parameter allows one to establish an analog of the averaging principle. We apply methods of the theory of fractional analysis and the theory of topological degree for condensing set-valued mappings.
About the authors
M. I. Kamenskii
Воронежский государственный университет
Author for correspondence.
Email: mikhailkamenski@mail.ru
Russian Federation, Воронеж
G. G. Petrosyan
Воронежский государственный университет инженерных технологий
Email: garikpetrosyan@yandex.ru
Russian Federation, Воронеж
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