A fractional dirac operator

Abstract

Based on the Riesz potential, S. Samko and coworkers studied the fractional integro-differentiation of functions of many variables which is a fractional power of the Laplace operator. We will extend this approach to a fractional Dirac operator based on the relation D = H (−Δ)−1/2. Because the Hilbert operator H is involved as well as the fractional Laplacian of order −1/2, we will use fractional Hilbert operators and fractional Riesz potentials for the construction.