Fractional Derivative Approach to the Self-gravitation Equation

Understand

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.