Higher derivative fermionic field equation in the first-order formalism

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 that extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is obtained, and minimal and nonminimal (anomalous) electromagnetic interactions of fermions are considered by introducing three phenomenological parameters. The Hamiltonian form of the first-order equation is obtained.