Ulam-Hyers stability and existence results for a coupled sequential Hilfer-Hadamard-type integrodifferential system

Subramanian Muthaiah; Manigandan Murugesan; Muath Awadalla; Bundit Unyong; Ria H. Egami; Subramanian Muthaiah; Manigandan Murugesan; Muath Awadalla; Bundit Unyong; Ria H. Egami

doi:10.3934/math.2024784

AIMS Mathematics

2024, Volume 9, Issue 6: 16203-16233. doi: 10.3934/math.2024784

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Ulam-Hyers stability and existence results for a coupled sequential Hilfer-Hadamard-type integrodifferential system

1.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, 641407, Tamilnadu, India
2.
Center for Computational Modeling, Chennai Institute of Technology, Chennai, 600069, Tamil Nadu, India
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
4.
Department of Mathematics and Statistics, Center of Excellence for Ecoinformatics, School of Science, Walailak University, Nakhon Si Thammarat 80160, Thailand
5.
Department of Mathematics, College of Science and Humanities in Sulail, Prince Sattam Bin Abdulaziz University, Saudi Arabia

Received: 01 March 2024 Revised: 13 April 2024 Accepted: 22 April 2024 Published: 08 May 2024
MSC : 34A08, 34B15, 45G15

This study aimed to investigate the existence, uniqueness, and Ulam-Hyers stability of solutions in a nonlinear coupled system of Hilfer-Hadamard sequential fractional integrodifferential equations, which were further enhanced by nonlocal coupled Hadamard fractional integrodifferential multipoint boundary conditions. The desired conclusions were obtained by using well-known fixed-point theorems. It was emphasized that the fixed-point technique was useful in determining the existence and uniqueness of solutions to boundary value problems. In addition, we examined the solution's Ulam-Hyers stability for the suggested system. The resulting results were further demonstrated and validated using demonstration instances.
- coupled integrodifferential system,
- sequential derivatives,
- Hadamard integrals,
- derivatives,
- Hilfer-Hadamard derivatives,
- multi-points,
- existence,
- uniqueness,
- Ulam-Hyers stability
Citation: Subramanian Muthaiah, Manigandan Murugesan, Muath Awadalla, Bundit Unyong, Ria H. Egami. Ulam-Hyers stability and existence results for a coupled sequential Hilfer-Hadamard-type integrodifferential system[J]. AIMS Mathematics, 2024, 9(6): 16203-16233. doi: 10.3934/math.2024784

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Abstract

This study aimed to investigate the existence, uniqueness, and Ulam-Hyers stability of solutions in a nonlinear coupled system of Hilfer-Hadamard sequential fractional integrodifferential equations, which were further enhanced by nonlocal coupled Hadamard fractional integrodifferential multipoint boundary conditions. The desired conclusions were obtained by using well-known fixed-point theorems. It was emphasized that the fixed-point technique was useful in determining the existence and uniqueness of solutions to boundary value problems. In addition, we examined the solution's Ulam-Hyers stability for the suggested system. The resulting results were further demonstrated and validated using demonstration instances.

References

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