Remarks on fractional derivatives

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grünwald–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. 2006 Elsevier Inc. All rights reserved.