Neutral stochastic functional differential evolution with varying-time delays driven by Rosenblatt process in Hilbert spaces

Abstract

In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by Rosenblatt process in a real separable Hilbert space. We prove an existence and uniqueness result of mild solution by means of the Banach fixed point principle. A practical example is provided to illustrate the viability of the abstract result of this work.