  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.
