Eigenfunctions and fundamental solutions for the Fractional Laplacian in 3 dimensions - Ferreira, Milton dos Santos (2016)
Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developed in \cite{FV}. We compute the fundamental solution for the three-parameter fractional Laplace operator $Δ^{(α,β,γ)}$ with $(α, β, γ) \in \,]0,1]^3$ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to \cite{FV} where it is also presented an operational approach based on the two Laplace transform.