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

Yazid Alhojilan; Hamdy M. Ahmed; Yazid Alhojilan; Hamdy M. Ahmed

doi:10.3934/math.2025562

AIMS Mathematics

2025, Volume 10, Issue 5: 12447-12463. doi: 10.3934/math.2025562

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

Yazid Alhojilan ^{1
,
,},
Hamdy M. Ahmed ²

1.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt

Received: 14 March 2025 Revised: 09 May 2025 Accepted: 22 May 2025 Published: 28 May 2025
MSC : 93C10, 34K37, 60J65, 93B05

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.
- Atangana-Baleanu fractional derivative,
- stochastic systems,
- mild solutions,
- control theory,
- Poisson random measures
Citation: Yazid Alhojilan, Hamdy M. Ahmed. Null controllability of Atangana-Baleanu fractional stochastic systems with Poisson jumps and fractional Brownian motion[J]. AIMS Mathematics, 2025, 10(5): 12447-12463. doi: 10.3934/math.2025562

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Abstract

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.

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