Space-time fractional derivative operators

DOI10.1090/S0002-9939-05-07949-9zbMath1070.47043MaRDI QIDQ4671866

Mark M. Meerschaert, Boris Baeumer, Jeff Mortensen

Publication date: 27 April 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

evolution equationsemigroupsanomalous diffusionfractional derivativestable probability distributions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Diffusion processes (60J60) Pseudodifferential operators (47G30)

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Cites Work

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• Fractional kinetic equation for Hamiltonian chaos
• Semigroups of linear operators and applications to partial differential equations
• Waiting-times and returns in high-frequency financial data: An empirical study
• Limit theorems for coupled continuous time random walks.
• A fractional diffusion equation to describe Lévy flights
• Stochastic solution of space-time fractional diffusion equations
• Random Walks on Lattices. II
• Limit theorem for continuous-time random walks with two time scales
• Fractional kinetic equations: solutions and applications
• Chance and Stability
• The random walk's guide to anomalous diffusion: A fractional dynamics approach