Existence and stability analysis of solutions for periodic conformable differential systems with non-instantaneous impulses

Yuanlin Ding; Yuanlin Ding

doi:10.3934/math.2025188

AIMS Mathematics

2025, Volume 10, Issue 2: 4040-4066. doi: 10.3934/math.2025188

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Research article

Existence and stability analysis of solutions for periodic conformable differential systems with non-instantaneous impulses

Yuanlin Ding ^,

School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, Jiangsu 213001, China

Received: 16 December 2024 Revised: 18 January 2025 Accepted: 06 February 2025 Published: 27 February 2025
MSC : 34A37, 34C25

This paper focuses on analyzing the existence and stability of solutions for periodic conformable systems with non-instantaneous impulses. First, we define the notion of the conformable Cauchy matrix to present solutions and demonstrate fundamental characteristics including periodicity and exponential estimation. Moreover, the effect of the non-instantaneous impulses on the exponential stability is comprehensively analyzed. Next, by applying the constant variation method, we can derive the solution for the linear nonhomogeneous system with non-instantaneous impulses. In addition, the existence of periodic solutions for the given linear nonhomogeneous system is investigated. Further, the conditions required to guarantee the existence and uniqueness of the periodic solutions for nonlinear systems are provided.
- conformable Cauchy matrix,
- conformable derivative,
- exponential stability,
- periodic solution
Citation: Yuanlin Ding. Existence and stability analysis of solutions for periodic conformable differential systems with non-instantaneous impulses[J]. AIMS Mathematics, 2025, 10(2): 4040-4066. doi: 10.3934/math.2025188

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Abstract

This paper focuses on analyzing the existence and stability of solutions for periodic conformable systems with non-instantaneous impulses. First, we define the notion of the conformable Cauchy matrix to present solutions and demonstrate fundamental characteristics including periodicity and exponential estimation. Moreover, the effect of the non-instantaneous impulses on the exponential stability is comprehensively analyzed. Next, by applying the constant variation method, we can derive the solution for the linear nonhomogeneous system with non-instantaneous impulses. In addition, the existence of periodic solutions for the given linear nonhomogeneous system is investigated. Further, the conditions required to guarantee the existence and uniqueness of the periodic solutions for nonlinear systems are provided.

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