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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 562691, 9 pages
http://dx.doi.org/10.1155/2014/562691
Research Article

Some Nonlinear Gronwall-Bellman-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications

1School of Science, Southwest University of Science and Technology, Mianyang 621010, China
2School of Business, Sichuan University, Chengdu 610064, China
3School of Preparatory Education, Southwest University for Nationalities, Chengdu 610041, China

Received 17 March 2014; Accepted 23 April 2014; Published 13 May 2014

Academic Editor: Robert A. Van Gorder

Copyright © 2014 Kelong Cheng 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 Gronwall-Bellman-Gamidov type integral inequalities with power nonlinearity and their weakly singular analogues are established, which can give the explicit bound on solution of a class of nonlinear fractional integral equations. An example is presented to show the application for the qualitative study of solutions of a fractional integral equation with the Riemann-Liouville fractional operator.