From Lévy walks to fractional material derivative: pointwise representation and a numerical scheme

DOI10.1016/J.CNSNS.2024.108316zbMATH Open1548.35287MaRDI QIDQ6604235

Marek Teuerle, Łukasz Płociniczak

Publication date: 12 September 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

zbMATH Keywords

finite volume methodRiemann-Liouville fractional derivativeLévy walkfractional material derivativesubordinated processcoupled continuous-time random walk

Mathematics Subject Classification ID

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Cites Work

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• Fractional governing equations for coupled random walks
• Langevin picture of Lévy walks and their extensions
• Limit theorems and governing equations for Lévy walks
• Stochastic representation of subdiffusion processes with time-dependent drift
• Triangular array limits for continuous time random walks
• Random walks with infinite spatial and temporal moments
• The problem of the random walk.
• From continuous time random walks to the generalized diffusion equation
• Convolution quadrature revisited
• Limit theorems for coupled continuous time random walks.
• Method of calculating densities for isotropic ballistic Lévy walks
• Linear Galerkin-Legendre spectral scheme for a degenerate nonlinear and nonlocal parabolic equation arising in climatology
• Why fractional derivatives with nonsingular kernels should not be used
• A review of definitions of fractional derivatives and other operators
• Stochastic modeling in nanoscale biophysics: subdiffusion within proteins
• Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
• Einstein relation for random walks in random environments
• Asymptotic distributions of continuous-time random walks: A probabilistic approach
• Asymptotic properties and numerical simulation of multidimensional Lévy walks
• Stochastic-Process Limits
• Existence of Turing instabilities in a two-species fractional reaction-diffusion system
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Multidimensional Lévy walk and its scaling limits
• Random Walks on Lattices. II
• Cluster continuous time random walks
• Finite Volume Methods for Hyperbolic Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Lévy walk with parameter dependent velocity: Hermite polynomial approach and numerical simulation
• Conservative random walks in confining potentials
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Fast and Oblivious Convolution Quadrature
• First Steps in Random Walks
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• A linear Galerkin numerical method for a quasilinear subdiffusion equation

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