31 citations · 432 across the 52 of their papers we have counts for
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A fractional generalization of the classical lattice dynamics approach
T. M. Michelitsch, B. A. Collet, A. P. Riascos +2
We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power l…
Fractional Lattice Dynamics: Nonlocal constitutive behavior generated by power law matrix functions and their fractional continuum limit kernels
Thomas Michelitsch, Bernard Collet, Alejandro Riascos +2
We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law ma…
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…
Calculation of the Electroelastic Green's Function of the Hexagonal Infinite Medium
Thomas Michelitsch
The electroelastic 4 4 Green's function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form (e…
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…
Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit
Thomas Michelitsch, Bernard Collet, Andrzej Nowakowski +1
The 1D discrete fractional Laplacian operator on a cyclically closed (periodic) linear chain with finitenumber of identical particles is introduced. We suggest a "fractional el…