A discrete fractional Gronwall inequality

Some New Gronwall-Bellmann Type Discrete Fractional Inequalities Arising in the Theory of Discrete Fractional Calculus

In this paper, we present some new GronwallBellmann type discrete fractional sum inequalities, and based on them present some Volterra-Fredholm type discrete inequalities. These inequalities are of new forms compared with the existing results in the literature, and can be used in the research of boundedness and continuous dependence on the initial value for solutions of fractional difference eq...

On Gronwall Inequality

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

A generalized Gronwall inequality and its application to a fractional differential equation

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.

On an Inequality of Gronwall

In this paper, we obtain some new Gronwall-Bellman type integral inequalities, and we give an application of our results in the study of boundedness of the solutions of nonlinear integrodifferential equations.

A New Generalized Gronwall-Bellman Type Inequality