  In this work, a cosmological model inspired by string/M- theory with
fermionic field is taken into consideration. Here it is investigated whether
the introduction of a non-Dirac fermionic field--characterized by an
\textit{interaction term}--affects the cosmological evolution. The
self-interaction potential is considered as a combination of the scalar and
pseudo-scalar invariants. It is observed that the fermionic field under
consideration behaves like an inflation field for the early Universe and later
on, as a dark energy field. The late time acceleration becomes more prominent
by the addition of the interaction term. There is a slight decrease for the
inflation peak as well as for the energy density. We see that addition of
higher order terms to the fermionic part of Lagrangian does not significantly
change either the inflation or the late time acceleration behavior.
