A fractional matter sector for general relativity

Abstract

In this work, we construct a fractional matter sector for general relativity. In particular, we propose a suitable fractional anisotropy function relating both the tangential and radial pressure of a spherically symmetric fluid based on the Gr\"unwald-Letnikov fractional derivative. The system is closed by implementing the polytropic equation of state for the radial pressure. We solve the system of integro-differential equations by Euler's method and explore the behavior of the physical quantities, namely, the normalized density energy, the normalized mass function, and the compactness.