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 …

Fast and accurate identification of unknown pollution sources is a crucial and challenging
task in water resources management, in which the characteristics of unknown pollution …

Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an
exponential factor leads to tempered fractional derivatives and integrals. Tempered …

Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

Evolution equations containing fractional derivatives can provide suitable mathematical
models for describing anomalous diffusion and transport dynamics in complex systems that …

An open problem in the numerical solution of fractional partial differential equations (FPDEs)
is how to obtain high-order accuracy for singular solutions; even for smooth right-hand sides …

This paper derives physically meaningful boundary conditions for fractional diffusion
equations, using a mass balance approach. Numerical solutions are presented, and …

Brownian motion is the archetypal model for random transport processes in science and
engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long …

Solute transport in rivers is controlled by surface hydrodynamics and by mass exchanges
between the surface stream and distinct retention zones. This paper presents a residence …