Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 194, Pages 92–106
DOI: https://doi.org/10.36535/0233-6723-2021-194-92-106 (Mi into819) 		 
Representation of solutions of Volterra integro-differential equations with fractional-exponential kernels

V. V. Vlasov, N. A. Rautian

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.36535/0233-6723-2021-194-92-106
Abstract: In this paper, we study the asymptotic behavior of solutions of integro-differential equations on the basis of spectral analysis of their symbols. For this, we represent strong solutions of these equations as the sum of terms corresponding to the real and non-real parts of the spectrum of symbols of these equations.
Keywords: integro-differential equation, operator-function, spectral analysis.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00288a
This work was supported by the Russian Foundation for Basic Research (project No. 20-01-00288a).
Document Type: Article
UDC: 517.968.72
MSC: 47G20, 34K30, 47A56, 34K12
Language: Russian
Citation: V. V. Vlasov, N. A. Rautian, “Representation of solutions of Volterra integro-differential equations with fractional-exponential kernels”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 194, VINITI, Moscow, 2021, 92–106
Citation in format AMSBIB
\Bibitem{VlaRau21}
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Representation of solutions of Volterra integro-differential equations with fractional-exponential kernels
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 5
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 194
\pages 92--106
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into819}
\crossref{https://doi.org/10.36535/0233-6723-2021-194-92-106}
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