Analytical Solution to the Fractional Polytropic Gas Spheres

TL;DR

This paper develops a series solution for the fractional Lane-Emden equation using modified Riemann-Liouville derivatives, revealing that fractional models predict smaller stellar volumes and masses compared to classical models.

Contribution

It introduces a novel series solution for the fractional Lane-Emden equation and explores fractional stellar models with new physical insights.

Findings

Fractional star models have smaller volume and mass.

The series solution recovers classical results when fractional order approaches 1.

Fractional models provide new perspectives on stellar structure.

Abstract

Lane-Emden equation could be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic index and . In the present paper, a series solution for the fractional Lane-Emden equation is presented. The solution is performed in the frame of modified Rienmann Liouville derivatives. The obtained results recover the well-known series solutions when . Fractional model of n=3 has been calculated and mass-radius relation, density ratio, pressure ratio and temperature ratio have been investigated. We found that the fractional star has a smaller volume and mass than that of the integer star.