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
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.
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Transactions of the Moscow Mathematical Society, 2019, 80, 169–188
MSC: 47G20, 34K30, 47A56, 34K12
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
\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.
\jour Trans. Moscow Math. Soc.
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