Geodesic
On the averaging principle for semilinear fractional differential inclusions in a Banach space with a deviating argument and a small parameter
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 74-84

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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 $q\in(0,1)$, a small parameter, and a deviant argument. We assume that the linear part of the inclusion generates a $C_0$-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.
Keywords: Cauchy problem, differential inclusion, fractional derivative, small parameter, measure of noncompactness, condensing multioperator.
Mots-clés : deviant argument 
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     author = {M. I. Kamenskii and G. Petrosyan},
     title = {On the averaging principle for semilinear fractional differential inclusions in a {Banach} space with a deviating argument and a small parameter},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {74--84},
     publisher = {mathdoc},
     volume = {204},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_204_a7/}
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M. I. Kamenskii; G. Petrosyan. On the averaging principle for semilinear fractional differential inclusions in a Banach space with a deviating argument and a small parameter. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 74-84. http://geodesic.mathdoc.fr/item/INTO_2022_204_a7/