Pth moment stability and approximate controllability of NDEs with delayed impulses and time-varying delays driven by ƒBm

Pth moment stability and approximate controllability of neutral differential equations (NDEs) with delayed impulse and time-varying delays driven by fractional Brownian motion (fBm) with H ? (0, 1/2) are studied. Unlike the fBm with Hurst parameter H ? (1/2, 1) in most of the literature, the fBm with Hurst parameter H ? (0, 1/2) in this work. The delayed impulse here means time delay in impulse, and the delay is no more than the minimum value of impulsive intervals. Based on Lyapunov stability theory and analytic semigroup theory, combined with stochastic analysis methods and impulse integral inequalities, some conditions guaranteeing the pth moment stability of the mild solution are established. Afterward, approximate controllability conditions of the system are acquired by the Lebesgue-dominated convergence theorem. At last, the validity of secured results is verified by an example.