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http://hdl.handle.net/10773/27160
Title: | Fundamental solution for natural powers of the fractional Laplace and Dirac operators in the Riemann-Liouville sense |
Author: | Teodoro, A. Di Ferreira, M. Vieira, N. |
Keywords: | Fractional Clifford Analysis Fractional derivatives Fundamental solution Poisson's equation Laplace transform |
Issue Date: | Feb-2020 |
Publisher: | Springer |
Abstract: | In this paper, we study the fundamental solution for natural powers of the $n$-parameter fractional Laplace and Dirac operators defined via Riemann-Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation starting from the fundamental solutions of the fractional Laplace $\Delta_{a^+}^\alpha$ and Dirac $D_{a^+}^\alpha$ operators, admitting a summable fractional derivative. The family of fundamental solutions of the corresponding natural powers of fractional Laplace and Dirac operators are expressed in operator form using the Mittag-Leffler function. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/27160 |
DOI: | 10.1007/s00006-019-1029-1 |
ISSN: | 0188-7009 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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artigo52.pdf | 424.29 kB | Adobe PDF | View/Open |
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