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 …

The flow in porous media has received a great deal of attention due to its importance and
many unresolved problems in science and engineering such as geophysics, soil science …

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 …

We introduce a fractional Fokker-Planck equation describing the stochastic evolution of a
particle under the combined influence of an external, nonlinear force and a thermal heat …

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 …

We consider Lévy flights subject to external force fields. This anomalous transport process is
described by two approaches, a Langevin equation with Lévy noise and the corresponding …

We establish a connection between anomalous heat conduction and anomalous diffusion in
one-dimensional systems. It is shown that if the mean square of the displacement of the …

A fractional diffusion equation based on Riemann− Liouville fractional derivatives is solved
exactly. The initial values are given as fractional integrals. The solution is obtained in terms …

Nuclear magnetic resonance (NMR) techniques cover a broad range of length and time
scales on which dynamic properties of fluids confined in porous media can be investigated …

We study distributed-order time fractional diffusion equations characterized by multifractal
memory kernels, in contrast to the simple power-law kernel of common time fractional …