Fractional derivative approach to the self-gravitation equation

Abstract

A new formalism is presented for finding the equilibrium distribution functions for axisymmetric systems. The formalism, obtained by using the concept of fractional derivatives, generalizes the methods of Fricke, Kalnajs and Jiang & Ossipkov, and has the advantage that can be applied to a wide variety of models. We found that this approach can be applied to both tridimensional systems and 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, the Mestel disc and the stellar dynamical tori introduced by Ciotti et al. in 2004. © 2008 The Authors. Journal compilation © 2008 RAS.