OICC Press Mathematical Sciences 2251-7456 20 3 2026 09 30 Approximate Null Controllability of Atangana–Baleanu Fractional Stochastic Evolution Equations with Poisson Jumps and Fractional Brownian Motion 10.57647/mathsci.2026.2003.15 EN Yazid Alhojilan Department of Mathematics, College of Science, Qassim University, Saudi Arabia Journal Article 2026 09 30 This paper investigates the approximate null controllability of a class of Atangana–Baleanu fractional stochas-tic evolution equations in a separable Hilbert space, driven simultaneously by a fractional Brownian motion and a Poisson random measure. The system is governed by the Caputo-type Atangana–Baleanu fractional derivative of order ???? ∈ (1/2, 1), a linear operator generating an ????-resolvent family, a bounded linear con-trol operator, and nonlinear terms satisfying suitable growth and integrability conditions. Assuming that the associated linear system is approximately null controllable and imposing standard Carathéodory-type assump-tions on the nonlinearities, we derive sufficient conditions ensuring the approximate null controllability of the full nonlinear stochastic system in the mean-square sense. The analysis relies on the variation-of-constants formula associated with fractional resolvent families, mean-square estimates for stochastic integrals with re-spect to fractional Brownian motion and compensated Poisson random measures, and a Schauder fixed point argument in an appropriate space of stochastic processes. An illustrative example involving a controlled Atangana–Baleanu fractional stochastic partial differential equation with Dirichlet boundary conditions is provided to demonstrate the applicability of the abstract results.