  We have considered the effects of space and momentum noncommutativity
separately on the zitterbewegung (ZBW) phenomenon. In the space
noncommutativity scenario, it has been expressed that, due to the conservation
of momentum, the Fourier decomposition of the expectation value of position
does~not change. However, the noncommutative (NC) space corrections to the
magnetic dipole moment of electron, that was traditionally perceived to come
into play only in the first-order of perturbation theory, appear in the
leading-order calculations with the similar structure and numerically the same
order, but with an opposite sign. This result may explain why for large lumps
of masses, the Zeeman-effect due to the noncommutativity remains undetectable.
Moreover, we have shown that the $x$- and $y$-components of the electron
magnetic dipole moment, contrary to the commutative (usual) version, are
non-zero and with the same structure as the $z$-component. In the momentum
noncommutativity case, we have indicated that, due to the relevant external
uniform magnetic field, the energy-spectrum and also the solutions of the Dirac
equation are changed in $3+1$ dimensions. In addition, our analysis shows that
in $2+1$ dimensions, the resulted NC field makes electrons in the zero
Landau-level rotate not only via a cyclotron motion, but also through the ZBW
motion with a frequency proportional to the field, which doubles the amplitude
of the rotation. In fact, this is a hallmark of the ZBW in graphene that
provides a promising way to be tested experimentally.
