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.

scholarly journals Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Pang Denghao ◽  
Jiang Wei
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.

scholarly journals Finite-Time Stability of Fractional-Order BAM Neural Networks with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yuping Cao ◽  
Chuanzhi Bai
Keyword(s):  
Neural Networks ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Finite Time ◽  
Distributed Delay ◽  
Bam Neural Networks ◽  
Time Stability ◽  
Finite Time Stability ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality

Based on the theory of fractional calculus, the generalized Gronwall inequality and estimates of mittag-Leffer functions, the finite-time stability of Caputo fractional-order BAM neural networks with distributed delay is investigated in this paper. An illustrative example is also given to demonstrate the effectiveness of the obtained result.

scholarly journals Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

2020 ◽  
pp. 16-16
Author(s):  
Mihailo Lazarevic ◽  
Darko Radojevic ◽  
Stjepko Pisl ◽  
Guido Maione
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Test Procedure ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Extended Form ◽  
Finite Time Stability ◽  
Numerical Example

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.

scholarly journals Finite-time stability of linear stochastic fractional-order systems with time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lassaad Mchiri ◽  
Abdellatif Ben Makhlouf ◽  
Dumitru Baleanu ◽  
Mohamed Rhaima
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Stochastic Analysis ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Analysis Techniques ◽  
Generalized Gronwall Inequality ◽  
Stability Of The Solution

AbstractThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

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