Some results for Volterra integro-differential equations depending on derivative in unbounded domains

In this paper we study the existence of continuous solutions of an integro-differential equation in unbounded interval depending on derivative This paper extend some results obtained by the authors using the technique developed in their previous paper. This technique consists in introducing, in the given problems, a function q, belonging to a suitable space, instead of the state variable x. The fixed points of this function are the solutions of the original problem. In this investigation we use a fixed point theorem in Fréchet spaces.