Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/21845
 Title: Homogeneous (α, k) -polynomial solutions of the fractional riesz system in hyperbolic space Author: Orelma, HeikkiVieira, Nelson Felipe Loureiro Keywords: Hypermonogenic functionsLaplace-Beltrami fractional differential operatorCaputo fractional derivativeHyperbolic fractional Riesz systemHyperbolic 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 URI: http://hdl.handle.net/10773/21845 DOI: 10.1007/s11785-017-0666-4 ISSN: 1661-8254 Appears in Collections: CIDMA - ArtigosCHAG - Artigos

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