Self-gravitating anisotropic spheres and non-local equations of state through the fractional calculus

In this work, we study static, spherically symmetric anisotropic configurations that obey a non-local equation of state relating radial pressure and energy density. Non-locality is introduced via the Caputo fractional derivative. We analyze in detail the impact of the fractional parameter on the behavior of the material sector. We find that for some values of the parameter, the mass density, the radial and tangential pressures reach their maximum value at the center and decrease monotonically toward the surface, as expected. We analyze the maximum mass allowed by our solution thorough a M-R diagram. We find that, based on the parameters considered, the maximum mass is on the order of three solar masses for a radius of approximately 15.6 km. We also find that increasing the fractional parameter leads to an increase in the compactness of the star, from 0.19 to 0.28.