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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 562494, 15 pages
Research Article

On Riemann-Liouville and Caputo Derivatives

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Department of Mathematics, Zhongyuan University of Technology, Zhengzhou 450007, China
3Department of Electrical and Computer Engineering, Utah State University, Logan, UT 84322-4120, USA

Received 27 June 2010; Accepted 25 January 2011

Academic Editor: Daniel Czamanski

Copyright © 2011 Changpin Li 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.


Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in science and engineering.