Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/18083
Title: | Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives |
Author: | Ferreira, M. Vieira, N. |
Keywords: | Fractional partial differential equations Fractional Laplace and Dirac operators Caputo derivative Eigenfunctions Fundamental solution |
Issue Date: | 1-Jun-2017 |
Publisher: | Taylor & Francis |
Abstract: | In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator ${}^C\!\Delta_+^{(\alpha,\beta,\gamma)}:= {}^C\!D_{x_0^+}^{1+\alpha} +{}^C\!D_{y_0^+}^{1+\beta} +{}^C\!D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$ and the fractional derivatives ${}^C\!D_{x_0^+}^{1+\alpha}$, ${}^C\!D_{y_0^+}^{1+\beta}$, ${}^C\!D_{z_0^+}^{1+\gamma}$ are in the Caputo sense. Applying integral transform methods we describe a complete family of eigenfunctions and fundamental solutions of the operator ${}^C\!\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. The solutions are expressed using the Mittag-Leffler function. From the family of fundamental solutions obtained we deduce a family of fundamental solutions of the corresponding fractional Dirac operator, which factorizes the fractional Laplace operator introduced in this paper. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/18083 |
DOI: | 10.1080/17476933.2016.1250401 |
ISSN: | 1747-6933 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
artigo51.pdf | Documento Principal | 403.49 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.