Analysis of the fractional relativistic polytropic gas sphere.

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 Riemann Liouville (mRL) frame, we formulate the fractional TOV (FTOV) equations and introduce an analytical solution. Using power series expansions in solving FTOV equations yields a limited physical range to the convergent power series solution. Therefore, combining the two techniques of Euler-Abel transformation and Padé approximation has been applied to improve the convergence of the obtained series solutions. For all possible values of the relativistic parameters ([Formula: see text]), 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 [Formula: see text] and the fractional parameter ([Formula: see text]). For n = 1, the volume decreases when [Formula: see text] = 0.1 and then increases when [Formula: see text] = 0.2 and 0.3. The volume of the sphere reduces as both [Formula: see text] and [Formula: see text] 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 ([Formula: see text], [Formula: see text]). The situation is altered by lowering the fractional parameter; the mass limit increases to M = 1.63348 M at [Formula: see text] and [Formula: see text].