Open Access
Translator Disclaimer
2013 Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
Bin Zheng
J. Appl. Math. 2013: 1-8 (2013). DOI: 10.1155/2013/341706

Abstract

By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the literature. Then, we apply the results established to research the boundedness, uniqueness, and continuous dependence on the initial value for the solution to a certain fractional differential equation.

Citation

Download Citation

Bin Zheng. "Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/341706

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950622
MathSciNet: MR3108936
Digital Object Identifier: 10.1155/2013/341706

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.2013 • 2013
Back to Top