Results on optimal control of impulsive Hilfer fractional stochastic integro-differential equations

Doha A. Kattan; Hasanen A. Hammad; Doha A. Kattan; Hasanen A. Hammad

doi:10.3934/math.2026444

AIMS Mathematics

2026, Volume 11, Issue 4: 10811-10830. doi: 10.3934/math.2026444

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Research article

Results on optimal control of impulsive Hilfer fractional stochastic integro-differential equations

Doha A. Kattan ¹,
Hasanen A. Hammad ^{2
,
,}

1.
Department of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received: 23 February 2026 Revised: 04 April 2026 Accepted: 13 April 2026 Published: 20 April 2026
MSC : 26E25, 34A08, 37N35, 47H09

This paper addresses a class of Hilfer fractional stochastic nonlinear integro-differential equations incorporating impulsive effects and optimal control in Hilbert spaces. We first establish the existence of mild solutions, ensuring the solvability of the system through the application of fractional calculus, stochastic analysis, and fixed-point techniques. The analytical framework effectively manages the combined difficulties arising from nonlocal operators, stochastic perturbations, and impulsive dynamics. Subsequently, we formulate the associated optimal control problem and derive the necessary conditions for optimality. An illustrative example is provided to demonstrate the practicality and robustness of the theoretical results.
- fixed-point approach,
- Hilfer fractional operator,
- optimal control,
- impulsive term,
- differential equation
Citation: Doha A. Kattan, Hasanen A. Hammad. Results on optimal control of impulsive Hilfer fractional stochastic integro-differential equations[J]. AIMS Mathematics, 2026, 11(4): 10811-10830. doi: 10.3934/math.2026444

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Abstract

This paper addresses a class of Hilfer fractional stochastic nonlinear integro-differential equations incorporating impulsive effects and optimal control in Hilbert spaces. We first establish the existence of mild solutions, ensuring the solvability of the system through the application of fractional calculus, stochastic analysis, and fixed-point techniques. The analytical framework effectively manages the combined difficulties arising from nonlocal operators, stochastic perturbations, and impulsive dynamics. Subsequently, we formulate the associated optimal control problem and derive the necessary conditions for optimality. An illustrative example is provided to demonstrate the practicality and robustness of the theoretical results.

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