Discussion on exact null boundary controllability of nonlinear fractional stochastic evolution equations in Hilbert spaces

Null boundary controllability refers to the ability to drive the state of a dynamical system to zero by applying suitable control inputs on the boundary of the domain. This research investigates the sufficient conditions for the null boundary controllability of Atangana-Baleanu (A-B) fractional stochastic differential equations involving fractional Brownian motion (fBm) within Hilbert space. We employ various tools, including fractional analysis, compact semigroup theory, fixed point theorems, and stochastic analysis, to derive the desired results. An example is included to illustrate the application of our findings.