  We show, in the case of a special dipolar source, that electromagnetic fields
in fractional quantum mechanics have an unexpected space dependence:
propagating fields may have non-transverse components, and the distinction
between near-field zone and wave zone is blurred. We employ an extension of
Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with
currents $j^\nu$ conserved globally but not locally, we have derived in another
work the field equation $\partial_\mu F^{\mu \nu}=j^\nu+i^\nu$, where $i^\nu$
is a non-local function of $j^\nu$, called "secondary current". Y.\ Wei has
recently proved that the probability current in fractional quantum mechanics is
in general not locally conserved. We compute this current for a Gaussian wave
packet with fractional parameter $a=3/2$ and find that in a suitable limit it
can be approximated by our simplified dipolar source. Currents which are not
locally conserved may be present also in other quantum systems whose wave
functions satisfy non-local equations. The combined electromagnetic effects of
such sources and their secondary currents are very interesting both
theoretically and for potential applications.
