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

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