Controllability of Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion with Hurst Parameter Lesser than 1/2

TL;DR

This paper studies the controllability of complex stochastic integro-differential equations driven by fractional Brownian motion with low Hurst parameter, using resolvent operators and fixed point theory.

Contribution

It introduces new controllability results for neutral stochastic equations driven by fractional Brownian motion with Hurst parameter less than 1/2.

Findings

Established sufficient conditions for controllability.

Applied resolvent operator theory and Banach fixed point theorem.

Extended controllability analysis to fractional Brownian motion with H<1/2.

Abstract

In this article we investigate the controllability for neutral stochastic functional integro-differential equations with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than $1/2$ in a Hilbert space. We employ the theory of resolvent operators combined with the Banach fixed point theorem to establish sufficient conditions to prove the desired result