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.