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http://hdl.handle.net/10773/18083
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DC Field | Value | Language |
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dc.contributor.author | Ferreira, M. | pt |
dc.contributor.author | Vieira, N. | pt |
dc.date.accessioned | 2017-07-14T14:45:35Z | - |
dc.date.available | 2018-07-20T14:01:01Z | - |
dc.date.issued | 2017-06-01 | - |
dc.identifier.issn | 1747-6933 | pt |
dc.identifier.uri | http://hdl.handle.net/10773/18083 | - |
dc.description.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. | pt |
dc.language.iso | eng | pt |
dc.publisher | Taylor & Francis | pt |
dc.relation | FCT - UID/MAT/ 0416/2013 | pt |
dc.relation | FCT - IF/00271/2014 | pt |
dc.rights | openAccess | por |
dc.subject | Fractional partial differential equations | pt |
dc.subject | Fractional Laplace and Dirac operators | pt |
dc.subject | Caputo derivative | pt |
dc.subject | Eigenfunctions | pt |
dc.subject | Fundamental solution | pt |
dc.title | Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives | pt |
dc.type | article | pt |
dc.peerreviewed | yes | pt |
ua.distribution | international | pt |
degois.publication.firstPage | 1237 | pt |
degois.publication.issue | 9 | pt |
degois.publication.lastPage | 1253 | pt |
degois.publication.title | Complex Variables and Elliptic Equations | pt |
degois.publication.volume | 62 | pt |
dc.date.embargo | 2018-06-01T14:00:00Z | - |
dc.identifier.doi | 10.1080/17476933.2016.1250401 | pt |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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artigo51.pdf | Documento Principal | 403.49 kB | Adobe PDF | View/Open |
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