Analytical Solution to the Fractional Polytropic Gas Spheres

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.