In this article we review classical and recent results in anomalous diffusion and provide
mechanisms useful for the study of the fundamentals of certain processes, mainly in …

Over the past one hundred years, Brownian motion theory has contributed substantially to
our understanding of various microscopic phenomena. Originally proposed as a …

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

To characterize the Brownian motion in a bounded domain Ω, it is well known that the
boundary conditions of the classical diffusion equation just rely on the given information of …

Metal organic chemical vapor deposition (MOCVD) of group III nitrides on graphene
heterostructures offers new opportunities for the development of flexible optoelectronic …

Anomalous diffusion in various complex systems abounds in nature and spans multiple
space and time scales. Canonical characterization techniques that rely upon mean squared …

The concept of a fractional derivative is introduced to the predator-prey system to describe
the species anomalous superdiffusive process. To achieve this, a new class of predator-prey …

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 …

We study far from equilibrium transport of a periodically driven inertial Brownian particle
moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square …

We carry out a detailed study of the motion of particles driven by a constant external force
over a landscape consisting of a periodic potential corrugated by a small amount of spatial …