On the Ulam-type stability of impulsive differential equations with multiple time delays

Tunç C., Tunç O.

Arab Journal of Basic and Applied Sciences, vol.32, no.1, pp.490-504, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1080/25765299.2025.2588901
  • Journal Name: Arab Journal of Basic and Applied Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.490-504
  • Keywords: Gronwall type inequality, impulsive delay differential equation, multiple constant time delays, Ulam-type stability
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this article, we conduct a rigorous analysis of the Ulam-type stability of first-order impulsive delay differential equations (IP-D-D-Es) with multiple time-dependent delays. Employing a Gronwall-type integral inequality tailored for piecewise continuous functions, we derive two new theorems concerning the generalized Ulam–Hyers–Rassias (G-U-H-R) stability of the first-order IP-D-D-E incorporating several constant time delays. To illustrate the applicability of the theoretical results, a concrete example is presented. The outcomes of this study offer significant and complementary contributions to the qualitative theory of the IP-D-D-Es with multiple constant delays.