EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS

Ferreira, Milton dos Santos; Vieira, Nelson

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 developedin [3]. We compute the fundamental solution for the three-parameter fractional Laplace operator Δ 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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Ferreira, Milton dos Santos / Vieira, Nelson: EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS. 2015.

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