27 citations · 166 across the 21 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…
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…
A self-similar field theory for 1D linear elastic continua and self-similar diffusion problem
Thomas Michelitsch, Gérard A. Maugin, Rahman Mujibur +3
This paper is devoted to the analysis of some fundamental problems of linear elasticity in 1D continua with self-similar interparticle interactions. We introduce a self-similar con…
Dispersion Relations and Wave Operators in Self-Similar Quasi-Continuous Linear Chains
Thomas M. Michelitsch, Gérard A. Maugin, Franck C. G. A Nicolleau +2
We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-sim…