Geodesic
Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 26-33.

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A multipole expansion of the fundamental solution of the fractional degree of the Laplace operator is constructed in terms of the Gegenbauer polynomials. Based on the decomposition constructed and the idea of the fast multipole method, we propose a numerical algorithm for solving the fractional differential generalization of the Poisson equation in the two-dimensional and three-dimensional spaces.
Keywords: fractional Laplacian, fundamental solution, fast multipole method, numerical algorithm.
Mots-clés : multipole expansion 
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N. S. Belevtsov; S. Yu. Lukashchuk. Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 26-33. http://geodesic.mathdoc.fr/item/INTO_2020_176_a2/

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