A Controllability Problem for Causal Functional Inclusions with an Infinite Delay and Impulse Conditions

Authors

  • Maria Afanasova Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia
  • Valeri Obukhovskii Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia
  • Garik Petrosyan Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia; Research Center, Voronezh State University of Engineering Technologies, Voronezh, Russia

DOI:

https://doi.org/10.25728/assa.2021.21.3.1105

Keywords:

causal operator, functional inclusion, controllability problem, functional differential inclusion, fractional derivative, measure of non-compactness, fixed point, topological degree, condensing multioperator

Abstract

In this paper we study the controllability problem in a Banach space for various classes of functional inclusions with causal operators with an infinite delay, and impulse effects. Basing on the topological degree theory for condensing multimaps, we prove a global theorem on the existence of trajectories for systems governed by functional inclusions. As an application, we obtain generalizations of existence theorems for the controllability problem for a semilinear first order functional differential inclusions of this type and a semilinear functional differential inclusions of a fractional order 0 < q < 1.

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Published

2021-10-01

How to Cite

Afanasova, M., Obukhovskii, V., & Petrosyan, G. (2021). A Controllability Problem for Causal Functional Inclusions with an Infinite Delay and Impulse Conditions. Advances in Systems Science and Applications, 21(3), 40–62. https://doi.org/10.25728/assa.2021.21.3.1105

Issue

Vol. 21 No. 3 (2021): Advances in Systems Science and Applications

Section

Articles