Exponential decay in mean square of mean-field neutral stochastic integrodifferential evolution equations: global attracting set and fractional Brownian motion

This paper shows that a mean-field neutral stochastic integrodifferential equation (NSIDEs) with finite delay, driven by a fractional Brownian motion (fBm) with Hurst parameter H>12, has a mild solution that exists and is unique. We also demonstrate the global attracting sets and the mild solution's exponential decay. Prior to this work, the mean-field neutral stochastic functional differential equation's exponential decay and global attractive sets were not taken into account. To demonstrate the application of our findings, an example is given. The conclusion mentions the intriguing upcoming work.