The Existence for stochastic coupled systems on networks with time-varying delay driven by driven by Rosenblatt process with delay and poisson jumps

Stochastic Analysis

Abstract

We present some results on the existence and uniqueness of mild solutions for system of semilinear impulsive differential with infinite fractional Brownian motions. Our approach is based on Perov's fixed point theorem and a new version of Schaefer's fixed point theorem in generalized Banach spaces. Also, we investigate the relationship between mild and weak solutions.