  In this paper, we study non-local $F(R)$-mimetic gravity. We implement
mimetic gravity in the framework of non-local $F(R)$-theories of gravity. Given
some specific class of models and using a potential on the mimetic field, we
investigate some scenarios related to the early-time universe, namely the
inflation and the cosmological bounce, compatibly with Einstein's gravity with
cold dark matter at the late-time.
