Using a rather complicated approach, the authors define a differential operator that they claim to be of fractional order but that, in fact, can easily be seen to be just a multiple of the classical first derivative. Specifically, in the one-dimensional case, their operator is nothing but \(N^\alpha_x f(a) = \exp(a^{-\alpha}) f'(a)\), and the extension to the case of multivariate functions follows the usual strategy for partial derivatives. Some of the properties of this operator are derived, but in view of its simple relation to the classical differential operator, all of this is very straightforward.