Fractional calculus is an effective tool in incorporating the effects of
non-locality and memory into physical models. In this regard, successful
applications exist rang- ing from signal processing to anomalous diffusion and
quantum mechanics. In this paper we investigate the fractional versions of the
stellar structure equations for non radiating spherical objects. Using
incompressible fluids as a comparison, we develop models for constant density
Newtonian objects with fractional mass distributions or stress conditions. To
better understand the fractional effects, we discuss effective values for the
density, gravitational field and equation of state. The fractional ob- jects
are smaller and less massive than integer models. The fractional parameters are
related to a polytropic index for the models considered