On the averaging principle for semilinear fractional differential inclusions in a banach space with a deviating argument and a small parameter

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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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