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

Noorah Mshary; Hamdy M. Ahmed; Noorah Mshary; Hamdy M. Ahmed

doi:10.3934/math.2025256

AIMS Mathematics

2025, Volume 10, Issue 3: 5552-5567. doi: 10.3934/math.2025256

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

Noorah Mshary ^{1
,
,},
Hamdy M. Ahmed ²

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt

Received: 26 November 2024 Revised: 21 January 2025 Accepted: 19 February 2025 Published: 12 March 2025
MSC : 34K37, 60J65, 93B05, 93C10

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.
- boundary control,
- fractional analysis,
- stochastic analysis
Citation: Noorah Mshary, Hamdy M. Ahmed. Discussion on exact null boundary controllability of nonlinear fractional stochastic evolution equations in Hilbert spaces[J]. AIMS Mathematics, 2025, 10(3): 5552-5567. doi: 10.3934/math.2025256

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Abstract

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.

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