Existence and stability of solutions for Hadamard type fractional differential systems with $ p $-Laplacian operators on benzoic acid graphs

Yunzhe Zhang; Youhui Su; Yongzhen Yun; Yunzhe Zhang; Youhui Su; Yongzhen Yun

doi:10.3934/math.2025356

AIMS Mathematics

2025, Volume 10, Issue 4: 7767-7794. doi: 10.3934/math.2025356

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Existence and stability of solutions for Hadamard type fractional differential systems with $ p $-Laplacian operators on benzoic acid graphs

1.
School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, Jiangsu, China
2.
School of Science, Shenyang University of Technology, Shenyang 110870, Liaoning, China

Received: 13 February 2025 Revised: 19 March 2025 Accepted: 24 March 2025 Published: 02 April 2025
MSC : 34A08, 34B15, 34K37

Benzoic acid is mainly used in the preparation of sodium benzoate preservatives, as well as in the synthesis of drugs and dyes. Therefore, a thorough understanding of its properties is of utmost importance. This paper is mainly concerned with the existence of solutions for a class of Hadamard type fractional differential systems with $ p $-Laplacian operators on benzoic acid graphs. Meanwhile, the Hyers-Ulam stability of the systems is also proved. Furthermore, an example is presented on a formaldehyde graph to demonstrate the applicability of the conclusions obtained. The novelty of this paper lies in the integration of fractional differential equations with graph theory, utilizing the formaldehyde graph as a specific case for numerical simulation, and providing an approximate solution graph after iterations.
- fractional differential equation,
- benzoic acid graphs,
- Hyers-Ulam stability,
- numerical simulation
Citation: Yunzhe Zhang, Youhui Su, Yongzhen Yun. Existence and stability of solutions for Hadamard type fractional differential systems with $ p $-Laplacian operators on benzoic acid graphs[J]. AIMS Mathematics, 2025, 10(4): 7767-7794. doi: 10.3934/math.2025356

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Abstract

Benzoic acid is mainly used in the preparation of sodium benzoate preservatives, as well as in the synthesis of drugs and dyes. Therefore, a thorough understanding of its properties is of utmost importance. This paper is mainly concerned with the existence of solutions for a class of Hadamard type fractional differential systems with $ p $-Laplacian operators on benzoic acid graphs. Meanwhile, the Hyers-Ulam stability of the systems is also proved. Furthermore, an example is presented on a formaldehyde graph to demonstrate the applicability of the conclusions obtained. The novelty of this paper lies in the integration of fractional differential equations with graph theory, utilizing the formaldehyde graph as a specific case for numerical simulation, and providing an approximate solution graph after iterations.

References

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