A coupled hybrid Hadamard fractional system with strongly coupled two-point boundary conditions

Dalal Alhwikem; Salma Trabelsi; Dalal Alhwikem; Salma Trabelsi

doi:10.3934/math.2026826

AIMS Mathematics

2026, Volume 11, Issue 7: 20338-20363. doi: 10.3934/math.2026826

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A coupled hybrid Hadamard fractional system with strongly coupled two-point boundary conditions

Dalal Alhwikem ¹,
Salma Trabelsi ^{2
,
,}

1.
Department of Mathematics, College of Science, Qassim University, Burydah 52571, Saudi Arabia
2.
Department of Mathematics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa, 31982, Saudi Arabia

Received: 27 April 2026 Revised: 30 June 2026 Accepted: 02 July 2026 Published: 10 July 2026
MSC : 34A08, 34A12, 34B15, 47H10

In this paper, we investigated a coupled system of hybrid Hadamard fractional differential equations subject to strongly coupled non-separated two-point boundary conditions. By employing properties of Hadamard fractional calculus, the considered problem was transformed into an equivalent system of fractional integral equations. The existence of solutions was established through a Burton-type extension of Krasnoselśkii's fixed point theorem, while uniqueness was obtained via Banach's contraction principle under suitable Lipschitz-type assumptions. Furthermore, the Ulam–Hyers stability of the proposed system was analyzed, and explicit stability estimates were derived. The obtained results extend and complement several existing contributions on hybrid fractional differential systems by treating a Hadamard framework together with strongly coupled boundary interactions. Finally, illustrative examples are presented to demonstrate the applicability of the theoretical findings.
- Hadamard fractional derivative,
- hybrid fractional differential equations,
- coupled systems,
- fixed point theorem,
- existence and uniqueness,
- Ulam–Hyers stability
Citation: Dalal Alhwikem, Salma Trabelsi. A coupled hybrid Hadamard fractional system with strongly coupled two-point boundary conditions[J]. AIMS Mathematics, 2026, 11(7): 20338-20363. doi: 10.3934/math.2026826

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Abstract

In this paper, we investigated a coupled system of hybrid Hadamard fractional differential equations subject to strongly coupled non-separated two-point boundary conditions. By employing properties of Hadamard fractional calculus, the considered problem was transformed into an equivalent system of fractional integral equations. The existence of solutions was established through a Burton-type extension of Krasnoselśkii's fixed point theorem, while uniqueness was obtained via Banach's contraction principle under suitable Lipschitz-type assumptions. Furthermore, the Ulam–Hyers stability of the proposed system was analyzed, and explicit stability estimates were derived. The obtained results extend and complement several existing contributions on hybrid fractional differential systems by treating a Hadamard framework together with strongly coupled boundary interactions. Finally, illustrative examples are presented to demonstrate the applicability of the theoretical findings.

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