Stability of Neutral Functional Stochastic Integro-Differential Delay
Systems with Impulses
Abstract
In this research work the stability for neutral stochastic functional
integro differential delay systems (NSFIDDSs) with impulses driven by
fractional Brownian motion (fBm). The supremum norm,
It$\hat{o}$’s formula in stochastic settings in
infinite dimensional space and M\”{o}nch fixed point
theorem are effectively utilized to derive the result. The novelties of
this research are listed as (i) the work space is not
$\mathcal{R}$ but the abstract Banach space
$\mathcal{E}$. (ii) the nonlinear function $f$ is
not necessary jointly continuous and satisfies some weaker assumptions.
(iii) the property of Hausdroff measure of noncompactness (HMNC) is
adopted to prove the relatively compactness conditions. Finally, an
example is demonstrated to illustrate the applicability of the obtained
theoretical results.