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

Tunç C., Tunç O.

Arab Journal of Basic and Applied Sciences, cilt.32, sa.1, ss.490-504, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/25765299.2025.2588901
  • Dergi Adı: Arab Journal of Basic and Applied Sciences
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.490-504
  • Anahtar Kelimeler: Gronwall type inequality, impulsive delay differential equation, multiple constant time delays, Ulam-type stability
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.