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http://hdl.handle.net/10773/15637
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DC Field | Value | Language |
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dc.contributor.author | Ferreira, Milton | pt |
dc.contributor.author | Vieira, Nelson | pt |
dc.date.accessioned | 2016-06-02T14:24:11Z | - |
dc.date.available | 2018-07-20T14:00:54Z | - |
dc.date.issued | 2016-06 | - |
dc.identifier.issn | 1661-8254 | pt |
dc.identifier.uri | http://hdl.handle.net/10773/15637 | - |
dc.description.abstract | In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions. | pt |
dc.language.iso | eng | pt |
dc.publisher | Springer International Publishing | 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 | Riemann-Liouville derivatives and integrals of fractional order | pt |
dc.subject | Eigenfunctions and fundamental solution | pt |
dc.subject | Laplace transform | pt |
dc.subject | Mittag-Leffler function | pt |
dc.title | Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case | pt |
dc.type | article | pt |
dc.peerreviewed | yes | pt |
ua.distribution | international | pt |
degois.publication.firstPage | 1081 | pt |
degois.publication.issue | 5 | pt |
degois.publication.lastPage | 1100 | pt |
degois.publication.title | Complex Analysis and Operator Theory | pt |
degois.publication.volume | 10 | pt |
dc.date.embargo | 2017-06-01T14:00:00Z | - |
dc.identifier.doi | 10.1007/s11785-015-0529-9 | pt |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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artigo39_VF.pdf | 399.72 kB | Adobe PDF | View/Open |
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