Null controllability of Atangana-Baleanu fractional stochastic systems with Poisson jumps and fractional Brownian motion

Null controllability is an essential concept in control theory, guaranteeing that the state of a system can be controlled to reach zero. We focused on investigating the sufficient conditions for the null controllability of Atangana-Baleanu (A-B) fractional stochastic differential equations (SDEs) involving Poisson jumps and fractional Brownian motion (fBm) within Hilbert space, a significant area of research in control theory and stochastic analysis. We employed a combination of 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.