Impulsive neutral stochastic functional integro-differential equations with infinite delay driven by fBm

Abstract

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H∈(1/2,1) in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions, which include the classical Lipschitz conditions as special case. An example is provided to illustrate the theory. Some well-known results are generalized and extended.