Controllability and stability analysis of an oscillating system with two delays

Abstract

In the current article, controllability and stability analysis of a system of differential equations is investigated. The system is governed by semilinear impulsive differential equations of second order with two delays. Controllability is studied using Rothe's fixed point theory while stability analysis is carried out with the help of Grönwall inequality and some other conditions. Fixed point approach is incorporated in determination of uniqueness of solution.

On the Analysis of a Neutral Fractional Differential System with Impulses and Delays

“…Definition 4 (Exact Controllability [27]). System ( 1) is known to be exactly controllable on [0, τ] if, for every φ ∈ C([−h, 0]; Z), and ς 1 ∈ P C(I, Z), there exists ṽ ∈ P C(I, U) such that the solution ς(µ) of ( 1) corresponding to ṽ satisfies ς(0) = φ(0) and ς(τ) = ς 1 .…”

“…It is concerned with the behavior of a system in a specified time interval. In order to extract sufficient conditions for FTS, researchers can employ the Lyapunov technique, characteristic equation method, or Grönwall approach [20][21][22][23][24][25][26][27][28][29][30].…”

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

“…Rassias [38] generalized Ulam's stability (US) and named it as Hyers-Ulam-Rassias stability. Many mathematicians expanded the concept of stability to various classes of s [15,[39][40][41]. Many researchers' interest has recently been drawn to study fractional-order s.…”

Stability and controllability of nonautonomous neutral system with two delays

“…Therefore, it can be required in a number of applications such as optimization, numerical analysis, error analysis, biology, and economics. A number of approaches exist in literature regarding this topic [12][13][14][15][16][17][18].…”