  In this paper we investigate the accelerating and decelerating cosmological
models with non-linear spinor fields and non-minimal interaction of $f(R)$
gravity with a scalar field. We combine two different approaches to the
description of dark energy: modified gravity theory and introduction of the
additional fields. Solutions for the FRW universe with power-law scale factor
are reconstructed for the model under consideration with specific choice for
scalar and spinor potentials. It is explained the role of scalar and spinor
potentials as well as f(R) function for emergence of accelerating or
decelerating cosmology.

General Relativity and Quantum Cosmology