  F-essence is a generalization of the usual Dirac model with the nonstandard
kinetic term. In this paper, we introduce a new model of spinor cosmology
containing both Ricci scalar and the non minimally coupled spinor fields in its
action. We have investigated the cosmology with both isotropy and anisotropy,
where the equations of motion of FRW and Bianchi type-I spacetimes have been
derived and solved numerically. Finally the quantization of these models
through Wheeler-De Witt (WD) wave function has been discussed.
