From continuous time random walks to the fractional fokker-planck equation

By Eli Barkai, Ralf Metzler, Joseph Klafter. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

678 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cc0647e7f6abd142ecdf8c2815667dd2408302ec

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Citations in the corpus

Multiscaling fractional advection‐dispersion equations and their solutions (2003, neutral): “Res., 39(1), 1022, doi:10.1029/2001WR001229, 2003.”
Finite difference methods for two-dimensional fractional dispersion equation (2006, methodology): “Keywords: Two-dimensional fractional partial differential equation; Implicit Euler method; Multi-dimensional fractional PDE; Numerical fractional PDE; Alternating direction implicit methods for fractional problems”
Limit theorems for continuous-time random walks with infinite mean waiting times (2004, neutral): “Keywords: Operator self-similar process; continuous-time random walk 2000 Mathematics Subject Classification: Primary 60G50 Secondary 60K40”
VECTOR GRÜNWALD FORMULA FOR FRACTIONAL DERIVATIVES (2004, background): “Introduction Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27].”
Numerical solution of nonlinear partial quadratic integro‐differential equations of fractional order via hybrid of block‐pulse and parabolic functions (2018, background): “In recent years, many problems in physical science [1], hydrology [2], chemistry and biochemistry [3], medicine [4], and general transport theory can be solved by the fractional calculus approach, which gives attractive applications as a new modeling tool in a variety of scientific and engineering f”
Finite difference approximations for fractional advection-dispersion flow equations (2004, background): “Fractional derivatives have recently been applied to many problems in physics [3,7,8,10,16,19,20,22, 29,31,36], 5nance [14,25,28], and hydrology [2,4–6,33,34].”
Continuous-time random walk and parametric subordination in fractional diffusion (2007, neutral): “[4, 5 , 20, 34, 35, 36, 42, 51, 53, 54], and references therein.”
Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, background): “Related equations of importance are the space/time fractional diffusion equations, the fractional advection-diffusion equation [17, 18] for anomalous diffusion with sources and sinks, and the fractional FokkerPlanck equation [4] for anomalous diffusion in an external field, etc.”
Fractional vector calculus for fractional advection–dispersion (2006, background): “Fractional derivatives have recently been applied to many problems in physics [5–18], finance [15,19–22], and hydrology [23–28].”
Fractional Kinetics in Kac–Zwanzig Heat Bath Models (2004, background): “(5) Thus, we conclude that the FFPE does not apply to the GLE (3.”