On controllability for a system governed by a semilinear fractional functional differential inclusion with a nonconvex-valued right-hand side in a Banach space
Applicable Nonlinear Analysis, Volume 1, Issue 2, December 2024, Pages: 160–169
VALERI OBUKHOVSKII
Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia
GARIK PETROSYAN
Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh 394043, Russia
JEN-CHIH YAO
Research Center for Interneural Computing, China Medical University, Taichung 40447, Taiwan
Abstract
In this paper we study the controllability for a system governed by a fractional semilinear functional differential inclusion with an almost lower semicontinuous nonconvex-valued nonlinearity and a closed linear operator generating a \(\mathfrak C_0\)–semigroup in a separable Banach space. We define the multivalued operator in the space of continuous functions whose fixed points are generating solutions of the problem. By using the fixed point theory for condensing multivalued maps and the methods of fractional analysis we study the properties of this multioperator, in particular, we demonstrate that under certain conditions it is condensing w.r.t. an appropriate measure of noncompactness. This allows to present the controllability principle as the main result of the paper.
Cite this Article as
Valeri Obukhovskii, Garik Petrosyan, and Jen-Chih Yao, On controllability for a system governed by a semilinear fractional functional differential inclusion with a nonconvex-valued right-hand side in a Banach space, Applicable Nonlinear Analysis, 1(2), 160–169, 2024