Fractional derivatives generalization of Einstein's field equations

In this paper we set up a fractional generalization of Einstein's field equations based on fractional derivatives inside the geodesic action integral and obtained non-local fractional Einstein's field equations. More specifically, the total derivative of any generalized coordinate is considered to take the special form is a real parameter, is the classical derivative operator and is the modified left Riemann-Liouville fractional derivative operator so that the classical result of the calculus of variations is considered as a particular case. Many attractive astrophysical and cosmological solutions have been obtained and discussed in some details.