title: Fractional diffusion equation for an n-dimensional correlated Lévy walk.
abstract: Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally.
authors: Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom.|Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida 33612, USA.
authors: Jake P
authors: JP
authors: Taylor-King
authors: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.|School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
authors: Rainer
authors: R
authors: Klages
authors: School of Mathematics, The University of Manchester, Manchester, M13 9PL, United Kingdom.
authors: Sergei
authors: S
authors: Fedotov
authors: Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom.
authors: Robert A
authors: RA
authors: Van Gorder