On the Kuzmin model in fractional Newtonian gravity

Abstract

Fractional Newtonian gravity, based on the fractional generalization of Poisson's equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton's theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.