Journal of Applied Mathematics
Volume 2011 (2011), Article ID 754350, 25 pages
http://dx.doi.org/10.1155/2011/754350
Research Article

Explicit Bounds to Some New Gronwall-Bellman-Type Delay Integral Inequalities in Two Independent Variables on Time Scales

Fanwei Meng,1 Qinghua Feng,1,2 and Bin Zheng2

1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
2School of Science, Shandong University of Technology, Zibo 255049, China

Received 20 April 2011; Accepted 8 August 2011

Academic Editor: Bernard Geurts

Copyright © 2011 Fanwei Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which provide a handy tool in the research of qualitative and quantitative properties of solutions of delay dynamic equations on time scales. The established inequalities generalize some of the results in the work of Zhang and Meng 2008, Pachpatte 2002, and Ma 2010.