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

Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic Fractional Schr\"odinger Equation