LAUSR

In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace $$\Delta _{a^+}^\alpha $$ and Dirac $$D_{a^+}^\alpha $$ operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag–Leffler function.