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Title: Homogeneous (α, k) -polynomial solutions of the fractional riesz system in hyperbolic space
Author: Orelma, Heikki
Vieira, Nelson Felipe Loureiro
Keywords: Hypermonogenic functions
Laplace-Beltrami fractional differential operator
Caputo fractional derivative
Hyperbolic fractional Riesz system
Issue Date: Jun-2017
Publisher: Springer
Abstract: In this paper we study the fractional analogous of the Laplace-Beltrami equation and the Riesz system studied previously by H. Leutwiler , in $\BR^3$. In both cases we replace the integer derivatives by Caputo fractional derivatives of order $0 <\alpha <1$. We characterize the space of solutions of the fractional Laplace-Beltrami equation, and we calculate its dimension. We establish relations between the solutions of the fractional Laplace-Beltrami equation and the solutions of the fractional Riesz system. Some examples of the polynomial solutions will be presented. Moreover, the behaviour of the obtained results when $\alpha=1$ is presented, and a final remark about the consideration of Riemann-Liouville fractional derivatives instead of Caputo fractional derivatives is made.
Peer review: yes
DOI: 10.1007/s11785-017-0666-4
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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