27 citations · 43 across the 3 of their papers we have counts for
3 papers
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…
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…