In this work the energy spectrum and solutions of Dirac-Pauli equation for the charged and neutral fermions taking into account interaction of anomalous magnetic moment (AMM) of particles with external field in the presence of a cylindric-symmetrical magnetic field in Non-relativistic limit are obtained. The total probability of the beta-decay of polarized neutron in a strong external cylindrical symmetrical magnetic field with contribution of fermions anomalous magnetic moment is calculated.
