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

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 2 ð1=2; 1Þ 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. In this paper, we are concerned with the existence and uniqueness of the mild solution for the following impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard Wiener process and an independent fractional Brownian motion d xðtÞ þ gðt; x t Þ ½ Š ¼ A½xðtÞ þ gðt; x t ފdt þ R t