نتایج جستجو برای: Gronwall inequality

تعداد نتایج: 57412  

2002
QINGHUA MA LOKENATH DEBNATH

This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...

2017
TAOUFIK GHRISSI Taoufik Ghrissi Mohamed Ali Hammami

The integral inequalities occupy privileged position in the theory of differential and integral equations. In the recent years nonlinear integral inequalities have received considerable attention because of their important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. In 1919, Gronwall [4] introduced the famous Gronwall inequality in t...

Journal: :J. Applied Mathematics 2013
Bin Zheng Qinghua Feng Fanwei Meng

In this work, we investigate some new Gronwall-Bellman type dynamic inequalities on time scales in two independent variables, which provide a handy tool in deriving explicit bounds on unknown functions in certain dynamic equations on time scales. The established results generalize the main results on integral inequalities for continuous functions in [1] and their corresponding discrete analysis...

2011
MIHAILO LAZAREVIĆ

This paper gives sufficient conditions for finite time stability and stabilization for perturbed nonlinear (non)homogeneous fractional order systems with time-varying delay. New stability criteria for this class of fractional order systems were derived using a recently obtained generalized Gronwall inequality as well as “classical” Bellman-Gronwall inequality. Last, a numerical example is given...

2007
Haiping Ye Jianming Gao Yongsheng Ding

This paper presents a generalized Gronwall inequality with singularity. Using the inequality, we study the dependence of the solution on the order and the initial condition of a fractional differential equation. © 2006 Elsevier Inc. All rights reserved.

2005
JAMES ADEDAYO OGUNTUASE

In this paper, we obtained some new Gronwall-Bellman type integral inequalities and we give some consequences of our results.

2011
Mihailo Lazarević

In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order system...

2008
AURELIAN CERNEA

We prove a Filippov-Gronwall type inequality for solutions of a nonconvex secondorder differential inclusion of Sturm-Liouville type.

2013
J. Jagan Mohan JAGAN MOHAN

Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.

2013
Shi-you Lin

In this paper, we provide several generalizations of the Gronwall inequality and present their applications to prove the uniqueness of solutions for fractional differential equations with various derivatives.

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