Stability of hybrid differential equations in the sense of Hyers-Ulam using Gronwall lemma

Abstract

In this paper, for the first time, we use Gronwall?s lemma to show the Hyers-Ulam and Hyers-Ulam-Rassias stability of hybrid differential equations, offering a fresh and rigorous framework for studying these complex structures. Two examples are provided to illustrate the correctness of our method, and graphical illustrations are used to graphically represent the results.