On the Ulam-Type Stability of Impulsive Differential Equations With Multiple Time Delays

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. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.