An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

Abstract

In this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example.

Existence, stability and controllability results for a class of switched evolution system with impulses over arbitrary time domain

“…Furthermore, in Pervaiz et al. ( 2021 ), the authors studied the controllability and stability analysis of fractional delay dynamical systems with both instantaneous and non-instantaneous impulses on time scales. However, for the considered class of systems of this paper, this is the first attempt to deal with the controllability results on the arbitrary time domain.…”

“… 2020 ; Pervaiz et al. 2021 ). Particularly, in (András and Mészáros 2013 ), the authors studied the Ulam–Hyers stability of linear and nonlinear dynamic equations and integral equations on time scales by using the theory of Picard operators.…”

“…In (Pervaiz et al. 2021 ), the authors considered the finite-dimensional fractional delay dynamical systems with instantaneous and non-instantaneous impulses on time scales and studied the stability and controllability results. Further, some results related to stability and controllability for finite-dimensional switched dynamic systems on time scales were addressed in the literature (Kumar et al.…”

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

“…DDEs are a form of DEs in which the derivative of the unknown function at a specific period is provided in terms of values of the function at past periods. Announcing delays in models enriches the vitality of these models and allows a perfect interpretation of actual occurrences [2][3][4]. DDEs arise frequently in various physical occurrences.…”

Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana–Baleanu–Caputo Derivative under Integral Boundary Conditions

“…Ulam discovered that the question of whether a proposition's claim genuinely obeys, or generally holds, if the hypothesis is slightly altered, is a prevalent and important one in many domains and has drawn the attention of many scholars. Tat is referred to as the Hyers-Ulam stability problem [32][33][34][35][36][37][38].…”