10.57647/mathsci.2026.2003.15

Approximate Null Controllability of Atangana–Baleanu Fractional Stochastic Evolution Equations with Poisson Jumps and Fractional Brownian Motion

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  • Yazid Alhojilan1,
  1. Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 2025-12-25

Revised: 2026-02-09

Accepted: 2026-02-11

Published in Issue 2026-09-30

Copyright (c) 2026 Yazid Alhojilan (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Alhojilan, Y. (2026). Approximate Null Controllability of Atangana–Baleanu Fractional Stochastic Evolution Equations with Poisson Jumps and Fractional Brownian Motion. Mathematical Sciences, 20(3). https://doi.org/10.57647/mathsci.2026.2003.15
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Abstract

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.

Keywords

  • Fractional Derivatives,
  • Approximate Null Controllability,
  • Stochastic Evolution Equations,
  • Fractional Brownian Motion,
  • Poisson Jumps,
  • Stochastic Systems
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