  A new formalism is presented for finding equilibrium distribution functions
for axisymmetric systems. The formalism, obtainded by using the concept of
fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs
(1972) and Jiang & Ossipkov (2007), and has the advantage that can be applied
to a wider variety of models. We found that this approach can be applied both
to tridimensional systems and to flat systems, without the necessity of dealing
with a pseudo-volume mass density. As an application, we obtain the
distribution functions of the Binney's logarithmic model and of the Mestel
disc.
