Mean-square stability analysis of stochastic delay evolution equations driven by fractional brownian motion with hurst index h (0,1)

In this paper, we consider stochastic evolution equations with finite delay driven by fractional Brownian motion (fBm) with Hurst index H is an element of (0, 1). First, the global existence and uniqueness of mild solutions are established by using a temporally weighted norm, the semigroup theory, the Banach fixed point theorem, and a new estimate of the stochastic integral with respect to fBm. Then after extending the integral inequality to the general case, we obtain the mean-square exponential stability of mild solutions. In particular, the convolution method and the Young convolution inequality are utilized to deal with the difficulty of the noise term caused by fBm with Hurst index H is an element of (0, 1). Finally, the stochastic evolution equation with multiple time-varying delays and the reaction diffusion neural networks system with time-varying delay are considered, and the global existence, uniqueness and exponential stability of mild solutions are proved by using the abstract results.