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Showing 2015 · math-phShow all
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math-ph2015★ 12 cited
Lattice fractional Laplacian and its continuum limit kernel on the finite cyclic chain
Thomas Michelitsch, Bernard Collet, Andrzej Nowakowski +1
The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length.We obt…
math-ph2015★ 15 cited
A regularized representation of the fractional Laplacian in n dimensions and its relation to Weierstrass-Mandelbrot type fractal functions
Thomas Michelitsch, Gérard Maugin, Shahram Derogar +1
We demonstrate that the fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with {\it self-similar} interparticle interactions. We show that the…