Commutativity of the Leibniz rules in fractional calculus

Many earlier works on the subject of fractional calculus (that is, differen tiation and integration of an arbitrary real or complex order) provide inte resting accounts of the theory and applications of fractional calculus oper ators in several areas of mathematical analysis (such as ordinary and parti al differential equations, integral equations, special functions, summation of series, etc.). The main object of this sequel to the aforementioned wor ks is to examine rather closely the commutativity of the familiar Leibniz r ules for fractional calculus and its various consequences. Some generalizat ions of a recent result of Tu, Chyan and Wu [1], involving fractional integ ration of powers of the logarithmic functions, are also considered. (C) 200 0 Elsevier Science Ltd. All rights reserved.