The fractional Laplacian as a limiting case of a self-similar spring model and applications to \(n\)-dimensional anomalous diffusion

DOI10.2478/s13540-013-0052-5zbMath1314.35209OpenAlexW1988412293MaRDI QIDQ2347376

Mujibur Rahman, Franck C. G. A. Nicolleau, Andrzej F. Nowakowski, Gérard A. Maugin, Thomas M. Michelitsch

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-013-0052-5

zbMATH Keywords

continuum limitFokker-Planck equationself-similarityfractional calculusfractalsanomalous diffusionscale invariancepower lawsfractional Laplaciannon-localityWeierstrass-Mandelbrot functionLévi (stable) distributionsLévi flights

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Diffusion processes (60J60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Self-similar stochastic processes (60G18) Fractals (28A80) Fractional partial differential equations (35R11) Fokker-Planck equations (35Q84)

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