We investigate the spatiotemporal nonlocality underlying fractional-derivative models as a
possible explanation for regional-scale anomalous dispersion with heavy tails. Properties of …

In this paper, we consider a variable-order fractional advection-diffusion equation with a
nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the …

Fractional advection–dispersion equations (FADEs) have been widely used in hydrological
research to simulate the anomalous solute transport in surface and subsurface water …

A one dimensional fractional diffusion model with the Riemann–Liouville fractional
derivative is studied. First, a second order discretization for this derivative is presented and …

The fractional advection–dispersion equation (FADE) known as its non-local dispersion, has
been proven to be a promising tool to simulate anomalous solute transport in groundwater …

Field and numerical experiments of solute transport through heterogeneous porous and
fractured media show that the growth of contaminant plumes may not exhibit constant …

This study proposed a new mobile‐immobile model (MIM) to describe reactive solute
transport with scale‐dependent dispersion in heterogeneous porous media. The model was …

The use of the conventional advection diffusion equation in many physical situations has
been questioned by many investigators in recent years and alternative diffusion models …

To model the observed local variation of transport speed, an extension of the homogeneous
space‐fractional advection‐dispersion equation (fADE) to more general cases with space …

The fractional derivative of order α, with 1< α≤ 2 appears in several diffusion problems used
in physical and engineering applications. Therefore to obtain highly accurate …