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Title: Some results in fractional Clifford analysis
Author: Vieira, Nelson Felipe Loureiro
Keywords: Fractional monogenic polynomials
Fischer decomposition
Fractional Dirac operator
Riemann-Liouville fractional derivative
Stationary transport operator
Issue Date: Aug-2015
Publisher: Bauhaus-University Weimar
Abstract: What is nowadays called (classic) Clifford analysis consists in the establishment of a function theory for functions belonging to the kernel of the Dirac operator. While such functions can very well describe problems of a particle with internal $SU(2)$-symmetries, higher order symmetries are beyond this theory. Although many modifications (such as Yang-Mills theory) were suggested over the years they could not address the principal problem, the need of a $n$-fold factorization of the d'Alembert operator. In this paper we present the basic tools of a fractional function theory in higher dimensions, for the transport operator $(\alpha =\alfa)$, by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed.
Peer review: yes
ISSN: 1611-4086
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Appears in Collections:CIDMA - Comunicações
CHAG - Comunicações

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