Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/16281
Title: Eigenfunctions and fundamental solutions for the Fractional Laplacian in 3 dimensions
Author: Ferreira, Milton dos Santos
Vieira, Nelson Felipe Loureiro
Keywords: Fractional Laplace operator
Riemann-Liouville fractional derivatives
Eigenfunctions
Fundamental solution
Mittag-Leffler function
Issue Date: Aug-2015
Publisher: Bauhaus-University Weimar
Abstract: 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 $\Delta^{(\alpha,\beta,\gamma)}$ with $(\alpha, \beta, \gamma) \in \,]0,1]^3$ 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.
Peer review: yes
URI: http://hdl.handle.net/10773/16281
ISSN: 1611-4086
Publisher Version: https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2451
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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