A NEW GRONWALL-BELLMAN TYPE INTEGRAL INEQUALITY AND ITS APPLICATION TO FRACTIONAL STOCHASTIC DIFFERENTIAL EQUATION

A New Generalized Gronwall-Bellman Type Inequality

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.

Brenstien polynomials and its application to fractional differential equation

The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Fractional difference inequalities of Gronwall – Bellman type

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.

Gronwall-Bellman-Type Integral Inequalities and Applications to BVPs

Chur-Jen Chen, Wing-Sum Cheung, and Dandan Zhao Department of Mathematics, Tunghai University, Taichung, Taiwan Correspondence should be addressed to Wing-Sum Cheung, [email protected] Received 9 May 2008; Revised 26 November 2008; Accepted 29 January 2009 Recommended by Alexander Domoshnitsky We establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. ...