Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion

Abstract The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions.