scholarly journals A Generalized Gronwall Inequality for Caputo Fractional Dynamic Delta Operator

2020 ◽  
Vol 6 (2) ◽  
pp. 129-136 ◽  
Keyword(s):  
Gronwall Inequality ◽  
Delta Operator ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality

scholarly journals A generalized discrete fractional Gronwall inequality and its application on the uniqueness of solutions for nonlinear delay fractional difference system

2018 ◽  
Vol 12 (1) ◽  
pp. 36-48 ◽  
Author(s):  
Jehad Alzabut ◽  
Thabet Abdeljawad
Keyword(s):  
Gronwall Inequality ◽  
Difference System ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Numerical Example ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality ◽  
Nonlinear Delay

In this paper, we state and prove a new discrete fractional version of the generalized Gronwall inequality. Based on this, a particular version expressed by means of discrete Mittag-Leer functions is provided. As an application, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo fractional difference system. Numerical example is presented to demonstrate the applicability of the main results.

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.

The Gronwall inequality for weighted integrals

1971 ◽  
Vol 30 (3) ◽  
pp. 504-504 ◽  
Author(s):  
F. M. Wright ◽  
M. L. Klasi ◽  
D. R. Kennebeck
Keyword(s):  
Gronwall Inequality ◽  
Grönwall Inequality ◽  
Weighted Integrals

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>

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