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.