  In this paper, we study the model of the late universe with the homogeneous,
isotropic and flat Friedmann-Robertson-Walker metric, where the source of the
gravitational field is based on the fermion and boson field, with the Maxwell
term $F_{\mu\nu}F^{\mu\nu} $ in four dimensions. The actuation of the Maxwell
term for the Einstein gravity makes it possible to find new approaches to solve
the problem of the observed accelerated expansion of the universe. Energy
conditions have been obtained and studied. These conditions impose very simple
and model-independent restrictions on the behaviour of energy density and
pressure since they do not require a specific equation of state of matter. To
consider the model, the energy conditions NEC, WEC, DEC are realized, and the
SEC condition is violated. The boson and fermion fields are responsible for the
accelerated regime at early times, but since the total pressure is tending
toward zero for large times, a transition to a decelerated regime occurs.
Maxwell field is crucial only in the early times.
