Geodesic
Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 197-220

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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. 
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     author = {V. V. Vlasov and N. A. Rautian},
     title = {Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {197--220},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a4/}
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V. V. Vlasov; N. A. Rautian. Spectral analysis and representation of solutions of integro-differential equations with fractional exponential kernels. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 197-220. http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a4/