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Stability of Neutral Functional Stochastic Integro-Differential Delay Systems with Impulses
  • DHANALAKSHMI K,
  • P. Balasubramaniam
DHANALAKSHMI K
The Gandhigram Rural Institute Deemed University Department of Mathematics
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P. Balasubramaniam
The Gandhigram Rural Institute Deemed University Department of Mathematics

Corresponding Author:[email protected]

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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.