# Conformable Fractional Polytropic Gas Spheres

## TL;DR

This paper introduces an analytical solution to the fractional polytropic gas sphere using conformable fractional derivatives, providing new models that differ from traditional solutions and exploring their physical properties.

## Contribution

It presents a novel analytical approach to fractional polytropic gas spheres with conformable derivatives, extending classical models and analyzing their physical parameters.

## Key findings

- Fractional models have smaller volume and mass than classical and other fractional models.
- The solution recovers known solutions when fractional order =1.
- Physical parameters vary with fractional order, affecting star structure.

## Abstract

Lane Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics. This differential equation suffers from the singularity at the center and has an exact solution only for the polytropic index n=0,1 and 5. In the present paper, we present an analytical solution to the fractional polytropic gas sphere via accelerated series expansion. The solution is performed in the frame of conformable fractional derivatives. The calculated models recover the well-known series of solutions when \alpha=1. Physical parameters such as mass-radius relation, density ratio, pressure ratio and temperature ratio for different fractional models have been calculated and investigated. We found that the present models of the conformable fractional stars have smaller volume and mass than that of both the integer star and fractional models performed in the frame of modified Rienmann Liouville derivatives.

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Source: https://tomesphere.com/paper/1907.02009