Incompressible Stars and Fractional Derivatives

TL;DR

This paper explores fractional calculus applied to stellar structure equations, revealing that fractional models of incompressible stars are smaller and less massive than classical models, with fractional parameters linked to polytropic indices.

Contribution

It develops fractional models of non-radiating spherical stars, providing insights into how fractional calculus affects stellar properties and structure.

Findings

Fractional models produce smaller, less massive stars.

Fractional parameters relate to polytropic indices.

Fractional effects alter density and gravitational field values.

Abstract

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.