Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense (Q2301503)

The paper deals with \(n\)-parameter fractional Laplace operators defined over \(n\)-dimensional space and the associated fractional Dirac operators over a Clifford algebra. The authors obtain the solution to the Poisson equation for \(n\)-parameter the fractional Laplace operator. On its base they construct the family of fundamental solutions of the natural powers of the \(n\)-parameter fractional Laplace operator as well as of the natural powers of the \(n\)-parameter fractional Dirac operator.