scholarly journals Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach

2022 ◽  
Vol 412 ◽  
pp. 126589
Author(s):  
Zhiguo Yan ◽  
Min Zhang ◽  
Gaizhen Chang ◽  
Hui Lv ◽  
Ju H. Park
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Gronwall Inequality ◽  
Annular Domain ◽  
Poisson Jumps ◽  
Grönwall Inequality ◽  
Stability And Stabilization ◽  
Domain Stability

scholarly journals Finite-time stability of $ q $-fractional damped difference systems with time delay

2021 ◽  
Vol 6 (11) ◽  
pp. 12011-12027
Author(s):  
Jingfeng Wang ◽  
◽  
Chuanzhi Bai
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
The Novel ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Grönwall Inequality ◽  
Uniqueness Of The Solution

<abstract><p>In this paper, we investigate and obtain a new discrete $ q $-fractional version of the Gronwall inequality. As applications, we consider the existence and uniqueness of the solution of $ q $-fractional damped difference systems with time delay. Moreover, we formulate the novel sufficient conditions such that the $ q $-fractional damped difference delayed systems is finite time stable. Our result extend the main results of the paper by Abdeljawad et al. [A generalized $ q $-fractional Gronwall inequality and its applications to nonlinear delay $ q $-fractional difference systems, J.Inequal. Appl. 2016,240].</p></abstract>

scholarly journals Finite time stability of linear fractional order dynam-ical system with variable delays

2018 ◽  
Vol 7 (2) ◽  
pp. 27
Author(s):  
Jackreece P. C ◽  
Aniaku S. E
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Finite Time ◽  
Gronwall Inequality ◽  
Sufficient Condition ◽  
Variable Delay ◽  
Time Stability ◽  
Finite Time Stability ◽  
Variable Delays ◽  
Grönwall Inequality

In this paper, some sufficient condition ensuring finite time stability are derived for a class of linear fractional order dynamical system with variable delay using generalized Gronwall inequality as well as classical Bellman-Gronwall inequality.

scholarly journals Finite-Time Stability of Solutions for Nonlinear q -Fractional Difference Coupled Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jingfeng Wang ◽  
Chuanzhi Bai
Keyword(s):  
Finite Time ◽  
Gronwall Inequality ◽  
Delay Systems ◽  
Stability Of Solutions ◽  
Stability Criteria ◽  
Time Stability ◽  
Fractional Difference ◽  
Finite Time Stability ◽  
Grönwall Inequality

In this paper, we investigate and prove a new discrete q -fractional version of the coupled Gronwall inequality. By applying this result, the finite-time stability criteria of solutions for a class of nonlinear q -fractional difference coupled delay systems are obtained. As an application, an example is provided to demonstrate the effectiveness of our result.

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