Geodesic
Representation of solutions of Volterra integro-differential equations with fractional-exponential kernels
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 194 (2021), pp. 92-106

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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. 
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     author = {V. V. Vlasov and N. A. Rautian},
     title = {Representation of solutions of {Volterra} integro-differential equations with fractional-exponential kernels},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {194},
     year = {2021},
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V. V. Vlasov; N. A. Rautian. Representation of solutions of Volterra integro-differential equations with fractional-exponential kernels. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 194 (2021), pp. 92-106. http://geodesic.mathdoc.fr/item/INTO_2021_194_a8/