Abstract:
In this article, we study the modified F (T ) gravity, which is non-minimally coupled to fermion fields in (2+1)
dimensional Friedmann-Robertson-Walker spacetime. By using the Lagrange multipliers method, the point-like Lagrangian
was derived and modified Friedmann equations, Dirac equations for the fermion fields were obtained. It is well-known that
the symmetry method of the Noether theorem is considered useful not only for establishing realistic cosmological models,
but also for finding exact solutions. Using the Noether theorem, the gravitational coupling, the self-consistent potential, the
symmetry generators, the form of F (T ) gravity and the first integral (Noether charge) or a conserved quantity for this model
are determined. Cosmological solutions with a power form describing the late time epoch of the Universe are obtained. The
Hubble parameter, the pressure and energy density for fermion fields and the equation of state parameter are found.
