The random walk's guide to anomalous diffusion: a fractional dynamics approach
Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type
are presented as a useful approach for the description of transport dynamics in complex …
are presented as a useful approach for the description of transport dynamics in complex …
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
Fractional dynamics has experienced a firm upswing during the past few years, having been
forged into a mature framework in the theory of stochastic processes. A large number of …
forged into a mature framework in the theory of stochastic processes. A large number of …
[BOOK][B] Mittag-Leffler functions, related topics and applications
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …
[BOOK][B] Theory and applications of fractional differential equations
AA Kilbas, HM Srivastava, JJ Trujillo - 2006 - books.google.com
This monograph provides the most recent and up-to-date developments on fractional
differential and fractional integro-differential equations involving many different potentially …
differential and fractional integro-differential equations involving many different potentially …
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …
have uncovered significant deviations from the laws of Brownian motion in a variety of …
[BOOK][B] Fractional calculus: an introduction for physicists
R Herrmann - 2011 - World Scientific
Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …
classes. In the following section we will present common generalizations for arbitrary …
From continuous time random walks to the fractional Fokker-Planck equation
We generalize the continuous time random walk (CTRW) to include the effect of space
dependent jump probabilities. When the mean waiting time diverges we derive a fractional …
dependent jump probabilities. When the mean waiting time diverges we derive a fractional …
Fractional dispersion, Lévy motion, and the MADE tracer tests
The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi
were conducted in a highly heterogeneous aquifer that violates the basic assumptions of …
were conducted in a highly heterogeneous aquifer that violates the basic assumptions of …
Boundary value problems for fractional diffusion equations
The fractional diffusion equation is solved for different boundary value problems, these
being absorbing and reflecting boundaries in half-space and in a box. Thereby, the method …
being absorbing and reflecting boundaries in half-space and in a box. Thereby, the method …
Matrix approach to discrete fractional calculus II: partial fractional differential equations
A new method that enables easy and convenient discretization of partial differential
equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays …
equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays …