  Many stellar configurations, including white dwarfs, neutron stars, black
holes, supermassive stars, and star clusters, rely on relativistic effects. The
Tolman-Oppenheimer-Volkoff (TOV) equation of the polytropic gas sphere is
ultimately a hydrostatic equilibrium equation developed from the general
relativity framework. In the modified Rieman Liouville (mRL) frame, we
formulate the fractional TOV (FTOV) equations and introduce an analytical
solution. Using power series expansions to solve the fractional TOV equations
yields a limited physical range to the convergent power series solution.
Therefore, the two techniques of Euler-Abel transformation and Pade
approximation have been combined to improve the convergence of the obtained
series solutions. For all possible values of the relativistic parameters
(\sigma), we calculated twenty fractional gas models for the polytropic indexes
n=0, 0.5, 1, 1.5, 2. Investigating the impacts of fractional and relativistic
parameters on the models revealed fascinating phenomena; the two effects for
n=0.5 are that the sphere's volume and mass decrease with increasing \sigma and
the fractional parameter (\alpha). For n=1, the volume decreases when
\sigma=0.1 and then increases when \sigma=0.2 and 0.3. The volume of the sphere
reduces as both \sigma and \alpha increase for n=1.5 and n=2. We calculated the
maximum mass and the corresponding minimum radius of the white dwarfs modeled
with polytropic index n=3 and several fractional and relativistic parameter
values. We obtained a mass limit for the white dwarfs somewhat near the
Chandrasekhar limit for the integer models with small relativistic parameters
(\alpha=1, \sigma=0.001). The situation is altered by lowering the fractional
parameter; the mass limit increases to Mlimit=1.63348 M at \alpha=0.95 and
\sigma=0.001.
