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. DiFerreira, M.Vieira, N. Keywords: Fractional Clifford AnalysisFractional derivativesFundamental solutionPoisson's equationLaplace 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 - ArtigosDMat - ArtigosCHAG - Artigos

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