Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion with Hurst parameter lesser than 1/2

Abstract In this study, we derive the necessary conditions for achieving controllability in a particular group of neutral stochastic integro-differential evolution equations. These equations are driven by a fractional Brownian motion with a Hurst parameter that is less than 1/2. To obtain these results, we utilize semigroup theory, resolvent operators, and a fixed-point technique. Furthermore, we provide an application of these findings to neutral partial integro-differential stochastic equations that have been perturbed by fractional Brownian motion.