Numerical approximation to the fractional derivative operator

In this paper we consider the numerical approximation of (A^{alpha }) by contour integral. We are mainly interested to the case of (A) representing the discretization of the first derivative by means of a backward differentiation formula, and ( 0! . The computation of the contour integral yields a rational approximation to (A^{alpha }) which can be used to define (k) -step formulas for the numerical integration of Fractional Differential Equations.