  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.
