Fractional Derivative Approach to the Self-gravitation Equation

Abstract

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.

5 pages, no figures, submitted to MNRAS

References in corpus (4)

• An Infinite Family of Generalized Kalnajs Disks
• Exact density-potential pairs from the holomorphic Coulomb field
• Two-integral distribution functions for axisymmetric systems
• Exact density-potential pairs from complex shifted axisymmetric systems

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