Eigenfunctions and fundamental solutions for the fractional Laplacian in 3 dimensions
Milton dos Santos Ferreira1,2, Nelson Felipe Loureiro Vieira2
1Instituto Politécnico de Leiria, Portugal; 2CIDMA, University of Aveiro, Portugal
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 . We compute the fundamental solution for the three-parameter fractional Laplace operator 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  where it is also presented an operational approach based on the two Laplace transform.
ISSN 1611 - 4086 | © IKM 2015