2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204365The 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 Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.remarks on fractional spin added, references added, in press Phys.Lett.AMathematical Physicstext