Analysis of the fractional relativistic isothermal gas sphere with application to neutron stars

Abstract The isothermal gas sphere model may be beneficial for understanding certain features of astrophysical objects like stars, but it has severe limits when used for compact stars. This study expands the Tolman–Oppenheimer–Volkoff (TOV) equation of the fractional relativistic gas sphere to contain fractional derivatives, resulting in a more general fractional TOV equation (FTOVI). The analytical solution of the FTOVI equation is tackled using an accelerated series expansion. We computed models for various relativistic ( σ ) and fractional ( α ) parameters. Models with α = 1 are retained to the relativistic integer models calculated by the integer version of the TOV equation. We examine the effects of the relativistic and fractional parameters on the Emden function, mass function, and the first derivative of the Emden function and the impact of these quantities on the pressure, density, and mass-radius relation. Investigating the central density-mass relation as an analog to neutron stars indicates that a maximum mass of the sphere exists, which further increases central density, resulting in instability and collapse. The observed mass and radius of three neutron stars and those predicted from the FTOVI models agreed well. The results of high-density fractional models demonstrate that fractional derivatives might drastically modify the expected mass and radius of neutron stars compared to integer models, indicating a possible need to reinterpret observational data of neutron stars via the lens of fractional calculus.