Contributed Talk

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 [3]. 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 [3] where it is also presented an operational approach based on the two Laplace transform.

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