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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2024, Volume 9, Issue 4, Pages 552–560
DOI: https://doi.org/10.47475/2500-0101-2024-9-4-552-560 (Mi chfmj402) 		 
Mathematics

Research on controllability issues for equations with the Hilfer derivative and with bounded operators in Banach spaces

D. M. Gordievskikha, V. E. Fedorovb

a Shadrinsk State Pedagogical University, Shadrinsk, Russia
b Chelyabinsk State University, Chelyabinsk, Russia
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DOI: https://doi.org/10.47475/2500-0101-2024-9-4-552-560
Abstract: The issues of approximate controllability of systems described by evolutionary equations in Banach spaces resolved with respect to the Hilfer fractional derivative are investigated. The operator at the unknown function is assumed to be bounded. Criteria of controllability for fixed and for free time is obtained. The abstract result is used when considering a class of distributed control systems of fractional order in time.
Keywords: Hilfer derivative, fractional order equation, Cauchy type problem, distributed control system, approximate controllability.
Funding agency Grant number
Поддержка научно-исследовательской деятельности по приоритетным направлениям научной деятельности вузов-партнёров 16-393
Russian Science Foundation 24-11-20002
The work of D.M.G. was carried out with the financial support of research works on priority areas of activity of partner universities of South Ural State University of Humanities and Education and Shadrinsk State Pedagogical University in 2024 on the topic "Study of controllability issues for Hilfer derivative equations and bounded operators in Banach spaces" (no. 16-393 dated May 2, 2024), V.E.F.'s work was supported by a grant from the Russian Scientific Foundation and the Government of the Chelyabinsk region, project 24-11-20002.
Received: 22.05.2024
Revised: 15.08.2024
Document Type: Article
UDC: 517.9
Language: Russian
Citation: D. M. Gordievskikh, V. E. Fedorov, “Research on controllability issues for equations with the Hilfer derivative and with bounded operators in Banach spaces”, Chelyab. Fiz.-Mat. Zh., 9:4 (2024), 552–560
Citation in format AMSBIB
\Bibitem{GorFed24}
\by D.~M.~Gordievskikh, V.~E.~Fedorov
\paper Research on controllability issues for equations with the Hilfer derivative and with bounded operators in Banach spaces
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2024
\vol 9
\issue 4
\pages 552--560
\mathnet{http://mi.mathnet.ru/chfmj402}
\crossref{https://doi.org/10.47475/2500-0101-2024-9-4-552-560}
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