A vacuum solution of modified Einstein equations based on fractional calculus

Abstract In this work, we construct a modified version of the Einstein field equations for vacuum and spherically symmetric spacetime in terms Riemann–Liouville fractional derivative. The main difference between our approach other works is that ensure both classical differential solutions are exactly recovered limit when parameter turned off. We assume valid inside near horizon radius match solution at horizon. Our resembles Herrera–Witten strategy (Adv High Energy Phys 2018:3839103, 2018, https://doi.org/10.1155/2018/3839103 , arXiv:1806.07143 [gr-qc]), where authors constructed an alternative black hole by assuming hyperbolically matches exterior one point obtain that, depending on value parameter, can be interpreted as regular or gravastar. As final step, compute curvature scalars show everywhere