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.
Categories: math-ph math.MP