A fixed point and its asymptotic stability of the solution of a differential equation on the real half-line

Abstract

This research study aims to analyze the solvability of a differential equation in two ways. The first approach involves by applying of Darbo’s fixed point Theorem and the measure of noncompactness (MNC) technique, the second approach by using some fixed point theories within the space BC(R₊). Moreover, we establish the asymptotic stability of the solution and dependency on the initial data and on the some functions. Additionally, we delve into the study of Hyers-Ulam stability. Finally, some examples are provided to verify our investigation.