Modified Riemann-Liouville Approach to Field Theory and Particle Physics

Abstract

In this contribution we present our recent results where we have applied a modified form of Riemann-Liouville fractional derivative to build up a generalized fractional D’Alembertian and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution was obtained. We have also set up the coarse-grained formulation of a fractional Schr¨odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects up to the lowest order in momentum.