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 BDF formula, and $% 0<\alpha <1$. 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.
