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Tr. Mosk. Mat. Obs., 2019, Volume 80, Issue 2, Pages 197–220 (Mi mmo625)  

Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels

V. V. Vlasov, N. A. Rautian

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: The aim of the present paper is to study the asymptotic behavior of solutions of integro-differential equations based on spectral analysis of their symbols. To this end, we obtain representations of strong solutions of these equations in the form of a sum of terms corresponding to the real and nonreal parts of the spectrum of operator functions that are the symbols of these equations. The resulting representations are new for this class of integro-differential equations.

Key words and phrases: Integro-differential equation, operator function, spectral analysis.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
Russian Science Foundation 17-11-01215
Theorems 6 and 7 were proved with support by the Russian Science Foundation under grant 17-11-01215. Theorems 2 and 5 were proved with support by the Presidential Program for the State Support of Leading Scientific Schools under grant NSh-6222.2018.1.


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English version:
Transactions of the Moscow Mathematical Society, 2019, 80, 169–188

UDC: 517.968.72
MSC: 47G20, 34K30, 47A56, 34K12
Received: 12.05.2019

Citation: V. V. Vlasov, N. A. Rautian, “Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels”, Tr. Mosk. Mat. Obs., 80, no. 2, MCCME, M., 2019, 197–220; Trans. Moscow Math. Soc., 80 (2019), 169–188

Citation in format AMSBIB
\Bibitem{VlaRau19}
\by V.~V.~Vlasov, N.~A.~Rautian
\paper Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 2
\pages 197--220
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo625}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 169--188
\crossref{https://doi.org/10.1090/mosc/298}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083806510}


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