  The main goal of this paper is to set up the coarse-grained formulation of a
fractional Schr\"odinger equation that incorporates a higher (spatial)
derivative term which accounts for relativistic effects at a lowest order. The
corresponding continuity equation is worked out and we also identify the
contribution of the relativistic correction the quantum potential in the
coarse-grained treatment. As a consequence, in the classical regime, we derive
the sort of fractional Newtonian law with the quantum potential included and
the fractional conterparts of the De Broglies's energy and momentum relations.
