Remarks on fractional derivatives

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grunwald-Letnikov derivative, the Riemann-Liouville derivative and the Caputo derivative. Especially, we compare the Riemann-Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in translating the higher fractional-order differential systems into lower ones. Besides, we also compare the Riemann-Liouville derivative and the Caputo derivative with the classical derivative. (c) 2006 Elsevier Inc. All rights reserved.