On chain rule for fractional derivatives

For some types of fractional derivatives, the chain rule is suggested in the form D(x)(alpha)f (g(x)) = (D(g)(1)f(g))(g=g(x)) D(x)(alpha)g(x). We prove that performing of this chain rule for fractional derivative D-x(alpha) of order alpha means that this derivative is differential operator of the first order (alpha = 1). By proving three statements, we demonstrate that the modified Riemann-Liouville fractional derivatives cannot be considered as derivatives of non-integer order if the suggested chain rule holds. (C) 2015 Elsevier B.V. All rights reserved.