  The isothermal gas sphere is well known as a powerful tool to model many
problems in astrophysics, physics, chemistry, and engineering. This singular
differential equation has not an exact solution and solved only by numerical
and approximate methods. In the present paper and within the framework of the
Newtonian hydrostatic equilibrium, we have developed general analytical
formulations for the fractional isothermal gas sphere. To obtain analytical
expressions for mass, radius, and density, besides the fractional isothermal
gas sphere, we used the conformable fractional calculus. Using the series
expansion method, we obtained a general recurrences relation, which allows us
to determine the series coefficients. The comparison of the series solution
with the numerical ones for the fractional parameter \alpha=1 is good for
dimensional parameters up to x=3.2, beyond this value, the series diverges. We
applied a combination of Euler-Abel and Pade techniques to accelerate the
series, therefore accelerated series converge to the numerical desired value.
We analyzed some physical parameters of a typical model of the neutron stars
such as the mass-radius relation, density, and pressure ratio for different
models. We found that the current models of the conformable neutron stars had
smaller volumes and masses than both stars in the context of modified
Rienmann-Liouville derivatives as well as the integer one.
