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 |
Files in This Item:
File | Description | Size | Format | |
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IKM_2015_MN.pdf | 82.47 kB | Adobe PDF | View/Open |
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