On systems of differential inclusions of fractional order in Banach spaces

V. V. Obukhovskii^a, M. I. Kamenskii^b, G. Petrosyan^a, T. A. Ul'vacheva^a, S. Zeng<sup>c

a</sup> Faculty of Physics and Mathematics Voronezh State Pedagogical University, Voronezh, Russia
^b Faculty of Mathematics, Voronezh State University, Voronezh, Russia
^c National Center for Applied Mathematics in Chongqing School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

Abstract: We study systems of fractional differential inclusions in a Banach space whose right-hand sides are multivalued maps of Carathéodory type depending on time, a finite set of functions, and their derivatives. To solve the existence problem for solutions to such a system, we apply the theory of fractional mathematical analysis and the theory of topological degree for multivalued condensing maps.

Keywords: differential inclusion, fractional derivative, boundary value problem, measure of noncompactness, fixed point, condensing multimap.

UDC: 517.929

MSC: 35R30

Received: 05.02.2025
Revised: 05.02.2025
Accepted: 25.02.2025

DOI: 10.33048/smzh.2025.66.208

 English version: Siberian Mathematical Journal, 2025, 66:2, 303–314