Fifty years of hyporheic zone research have shown the important role played by the
hyporheic zone as an interface between groundwater and surface waters. However, it is only …

This paper outlines the various approaches used to calculate bedload transport. As bedload
transport exhibits considerable spatial and temporal variations, computing the bedload …

The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

This chapter is devoted to time-and space-nonlocal generalizations of the standard Fourier
law, the corresponding generalizations of the classical heat conduction equation and …

In this research, we deal with two types of inverse problems for diffusion equations involving
Caputo fractional derivatives in time and fractional Sturm-Liouville operator for space. The …

This paper deals with the numerical solution of classes of fractional convection–diffusion
equations with variable coefficients. The fractional derivatives are described based on the …

Fractional derivatives can be viewed either as handy extensions of classical calculus or,
more deeply, as mathematical operators defined by natural phenomena. This follows the …

The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are
transition densities of a stable Lévy motion, representing the accumulation of power-law …

Earth's surface is composed of a staggering diversity of particulate–fluid mixtures: dry to wet,
dilute to dense, colloidal to granular and attractive to repulsive particles. This material variety …

We provide a probabilistic definition of the bed load sediment flux. In treating particle
positions and motions as stochastic quantities, a flux form of the Master equation (a general …