Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic   Fractional Schr\"odinger Equation
  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. 
J. Weberszpil, C. F. L. Godinho, A. Cherman, J. A. Helay\"el-Neto
math-ph hep-th math.MP quant-ph