Gauge invariance in fractional field theories

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order in the coupling constant . 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 Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.