Conformable fractional polytropic gas spheres

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=0,1and 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 whenα=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.