Singular integro-differential equations of the special type in Banach spaces and it’s applications

In this paper Cauchy problem for singular integro-differential equation of the special type in Banach spaces is investigated with help of the theory of fundamental operator-functions. The corresponding fundamental operator-function is constructed, the conditions for equal generalized with classical solution are describet. The abstract results are illustrated by examples of the initial-bounbary problems of the mathematical theory of viscoelasticity.