STABILITY ANALYSIS ON ABSTRACT SECOND-ORDER FUNCTIONAL IMPULSIVE DIFFERENTIAL SYSTEMS WITH STATE-DEPENDENT DELAY

Abstract

The paper investigates Hyers-Ulam stability for impulsive second-order abstract functional differential systems with state-dependent delay. It derives its results from the framework of significantly constant cosine families of linear operators. The work establishes a number of definitions of Hyers-Ulam stability by utilising Gronwall’s type inequality and Lipschitz criteria. Theoretical derivations are proved by an example of a wave equation that successfully explains how the acquired results can be applied in practise. The study contributes to the understanding of stability occurrences in a specific class of functional differential systems by addressing complicated systems with impulsive dynamics and state-dependent delay, as well as by utilising rigorous mathematical techniques.