ABSTRACT
In this section we show how to write an integra-differential equation of Barbashin type as a differential equation in a suitable Banach space, and we discuss some problems occurring in this connection. Moreover, we study the evolution operator (Cauchy operator) ofthe resulting inhomogeneous differential equation which allows us to give an explicit integral representation of the solution of an initial value problem. Many contributions contained in this and the following sections are due to DIALLO [1988, 1988a, 1988b, 1989].
