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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 841718, 12 pages
http://dx.doi.org/10.1155/2014/841718
Research Article

A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China

Received 30 March 2014; Accepted 10 June 2014; Published 10 July 2014

Academic Editor: Turgut Öziş

Copyright © 2014 Jun Zhou. 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

We discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of the multiple Mittag-Leffler function. We apply the result to give continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation.