  The generalized Dirac equation of the third order, describing particles with
spin 1/2 and three mass states, is analyzed. We obtain the first order
generalized Dirac equation in the 24-dimensional matrix form. The mass and spin
projection operators are found which extract solutions of the wave equation
corresponding to pure spin states of particles. The density of the
electromagnetic current is obtained, and minimal and non-minimal (anomalous)
electromagnetic interactions of fermions are considered by introducing three
phenomenological parameters. The Hamiltonian form of the first order equation
has been obtained.
