2002/10/17 by Igor M. Sokolov, Ralf Metzler, Maria Gullo · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Diverse academic and cultural studies #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Nonlinear Differential Equations Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.67.010101
arxiv created 2002/10/17 · openalex publication_date 2005/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/28
Lévy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Lévy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Lévy walks, in which the fractional equivalent of the material derivative occurs. Our approach is expected to be useful for the dynamical formulation of Lévy walks in an external force field or in phase space, for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited.