  The principle of local gauge invariance is applied to fractional wave
equations and the interaction term is determined up to order $o(\bar{g})$ in
the coupling constant $\bar{g}$. As a first application, based on the
Riemann-Liouville fractional derivative definition, the fractional Zeeman
effect is used to reproduce the baryon spectrum accurately.
  The transformation properties of the non relativistic fractional
Schr\"odinger-equation under spatial rotations are investigated and an internal
fractional spin is deduced.
