In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator where the fractional derivatives are in the Caputo sense. Applying integral transform methods we describe a complete family of eigenfunctions and fundamental solutions of this operator in classes of functions admitting a summable fractional derivative. The solutions are expressed using the Mittag-Leffler function. From the family of fundamental solutions obtained we deduce a family of fundamental solutions of the corresponding fractional Dirac operator, which factorizes the fractional Laplace operator introduced in this paper.

Authors: Ferreira M, Vieira N

Published in: Complex Variables and Elliptic Equations