Please use this identifier to cite or link to this item: 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

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