Correct Solvability and Representation of Solutions of Volterra Integrodifferential Equations with Fractional Exponential Kernels
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For abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space, the correct solvability of initial value problems is studied and the spectral analysis of operator functions being symbols of these equations is performed. This makes it possible to represent strong solutions of the equations under consideration as series in exponentials corresponding to spectral points of the operator functions. The equations in question are abstract forms of linear partial integrodifferential equations arising in the theory of viscoelasticity and in a number of other important applications.
The part of this study concerning Theorems 1–3 was supported by RF President’s Grant for State Support of Leading Scientific Schools of the Russian Federation, project no. NSh-6222.2018.1). The part of this study concerning Theorems 4–9 was supported by the Russian Science Foundation, project no. 17-11-01215.
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