Stability and controllability of nonautonomous neutral system with two delays

Abstract

This article investigates the exact and approximate controllability, finite time stability, and scriptB$$ \mathcal{B} $$–Hyers–Ulam–Rassias stability of a neutral impulsive system of differential equations with two delays. Fixed point theory is associated in the analysis of controllability of the system. The stability analysis is carried out with the help of Grönwall type inequality.

Existence, uniqueness, and Hyers-Ulam stability of abstract neutral differential equation containing state-dependent fractional integrable impulses

“…Answers to Ulam's question, its attractions and inductions for various situations is an important area of research and is known as Ulam's stability. For detailed information about Ulam's stability, we recommend [12,30,31,34,35,37,[41][42][43][44] and references therein.…”

Analysis of coupled system of q‐fractional Langevin differential equations with q‐fractional integral conditions

“…Rassias [38] generalized Ulam's stability ( $$$ \mathtt{US} $$$) and named it as Hyers–Ulam–Rassias stability. Many mathematicians expanded the concept of stability to various classes of $$$ \mathcal{DE}s $$$ [15, 39–41]. Many researchers' interest has recently been drawn to study fractional‐order $$$ \mathcal{BVP}s $$$.…”