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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 226, Pages 80–88
DOI: https://doi.org/10.36535/0233-6723-2023-226-80-88 (Mi into1204) 		 
Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives

M. V. Plekhanovaab, G. D. Baybulatovab

a South Ural State University, Chelyabinsk
b Chelyabinsk State University
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DOI: https://doi.org/10.36535/0233-6723-2023-226-80-88
Abstract: In this paper, we consider a class of start control problems for systems whose states are described by equations in Banach spaces that are not solvable with respect to the highest Gerasimov–Caputo fractional derivative and depend nonlinearly on lower-order fractional derivatives. A theorem on the existence of an optimal control is obtained. Abstract results are applies to the study of the start control problem for the modified Sobolev equation with a fractional derivative in time.
Keywords: optimal control, start control, fractional differential equation, Gerasimov–Caputo derivative, nonlinear evolution equation, degenerate evolution equation.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-90015
Программа Президента РФ государственной поддержки ведущих научных школ НШ-2708.2022.1.1
This work was supported by the Russian Foundation for Basic Research (project No. 20-31-90015) and the Program of the President of the Russian Federation for State Support of Leading Scientific Schools (project NSh-2708.2022.1.1).
Document Type: Article
UDC: 517.16, 517.165
MSC: 26D15
Language: Russian
Citation: M. V. Plekhanova, G. D. Baybulatova, “Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 226, VINITI, Moscow, 2023, 80–88
Citation in format AMSBIB
\Bibitem{PleBay23}
\by M.~V.~Plekhanova, G.~D.~Baybulatova
\paper Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 226
\pages 80--88
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1204}
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