  In this paper we consider the numerical solution of Fractional Differential
Equations by means of $m$-step recursions. The construction of such formulas
can be obtained in many ways. Here we study a technique based on the rational
approximation of the generating functions of Fractional Backward
Differentiation Formulas (FBDFs). Accurate approximations allow to define
methods which simulate the theoretical properties of the underlying FBDF with
important computational advantages. Numerical experiments are presented.
