# Analytical solution to the fractional polytropic gas spheres

Research paper by Mohamed I. Nouh, Emad A-B. Abdel-Salam

Indexed on: 13 Apr '18Published on: 16 Apr '18Published in: The European Physical Journal Plus

#### Abstract

The Lane-Emden equation can be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic indices n = 0, 1 and 5. 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 $$\alpha =1$$. The fractional model of n = 3 is calculated and the mass-radius relation, density ratio, pressure ratio and temperature ratio are investigated. The fractional star appears much different than the integer star, as it is denser, more stressed and hotter than the integer star.