EXISTENCE AND HYERS-ULAM STABILITY OF IMPULSIVE DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Fengya Xu; Jing Shao; Zhihao Tian; Zhaowen Zheng

doi:10.11948/20240295

2025 Volume 15 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(5): 2589-2610

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Fengya Xu, Jing Shao, Zhihao Tian, Zhaowen Zheng. EXISTENCE AND HYERS-ULAM STABILITY OF IMPULSIVE DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2589-2610. doi: 10.11948/20240295

Citation:

Fengya Xu, Jing Shao, Zhihao Tian, Zhaowen Zheng. EXISTENCE AND HYERS-ULAM STABILITY OF IMPULSIVE DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2589-2610. doi: 10.11948/20240295

EXISTENCE AND HYERS-ULAM STABILITY OF IMPULSIVE DELAY INTEGRO-DIFFERENTIAL EQUATIONS

1.
Normal College, Shenyang University, Shenyang 110000, Liaoning, China
2.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, Guangdong, China

Author Bio: Email: 2862323093@qq.com(F. Xu); Email: 3316520764@qq.com(Z. Tian); Email: zhwzheng@126.com(Z. Zheng)
Corresponding author: Email: shaojing99500@163.com(J. Shao)
Fund Project: The authors were supported by Natural Science Foundation of China (No. 12301199), the basic scientific research project of higher education of Liaoning province (No. JYTMS20231164), Guangdong Provincial Featured Innovation Projects of High School (No. 2023KTSCX067) and Liaoning province innovation and entrepreneurship training program (No. S202411035066)

Abstract

Abstract

In recent years, impulsive ordinary differential equations with delay terms have garnered significant attention due to their wide applications in various fields, including mechanics, population dynamics, and nuclear reactor physics. The primary objective of this paper is to establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability for impulsive delay ordinary differential equations by employing a novel generalized Gronwall inequality alongside fixed-point methods and Picard's operator technique. An example is provided to illustrate the stability of impulsive differential equation which is based on a new deep learning framework, and the integral operators are learned using neural networks.
- Hyers-Ulam stability /
- Hyers-Ulam-Rassias stability /
- delay integro-differential equation /
- impulses
MSC: 26A33, 34A08, 34B27

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References

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