Electron. J. Differential Equations, Vol. 2020 (2020), No. 118, pp. 1-19.

Stability for conformable impulsive differential equations

Yuanlin Ding, Michal Feckan, Jinrong Wang

Abstract:
In this article, we study impulsive differential equations with conformable derivatives. Firstly, we derive suitable formulas for solving linear impulsive conformable Cauchy problems. Then, we show that the linear problem has asymptotic stability, and the nonlinear problem has generalized Ulam-Hyers-Rassias stability. Also we illustrate our results with examples.

Submitted October 4, 2020. Published December 8, 2020.
Math Subject Classifications: 34A37, 34A08, 34D20.
Key Words: Conformable derivative; impulsive differential equation; asymptotic stability; generalized Ulam-Hyers-Rassias stability.
DOI: 10.58997/ejde.2020.118

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Yuanlin Ding
Department of Mathematics
Guizhou University
Guiyang, Guizhou 550025, China
email: yldingmath@126.com
Michal Feckan
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University in Bratislava
Mlynsk\'a dolina, 842 48 Bratislava, Slovakia
email: Michal.Feckan@fmph.uniba.sk
Jinrong Wang
Department of Mathematics
Guizhou University
Guiyang, Guizhou 550025, China
email: wjr9668@126.com

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