Study of Volterra integro-differential equations by methods of semigroup theory

The abstract Volterra integro-differential equations are investigated, which are operator models of problems of viscoelasticity theory. The class of equations under consideration also includes the Gurtin–Pipkin integro-differential equations describing the process of heat propagation in media with memory. The sums of decreasing exponents or sums of Rabotnov functions with positive coefficients can be considered in particular as the kernels of integral operators, which are widely used in the theory of viscoelasticity and heat propagation theory.