FRW and Bianchi type I cosmology of f-essence

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.