Biological and psychological processes routinely break ergodicity, meaning they fail to have
stable means (M ean) and independent variation over time that we might find in additive …

The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times
and narrow distributed displacements with a non-zero mean, is a well studied model for …

The expanding medium is very common in many different fields, such as biology and
cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different …

We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian
center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two …

Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more
general version that is the GIADE equation with nonlinear source term, is discretized by …

We study the diffusive dynamics of a system in a nonlinear velocity-dependent frictional
environment within a continuous time random walk model. In this model, the motion is …

Reaction-diffusion equations are widely used as the governing evolution equations for
modeling many physical, chemical, and biological processes. Here we derive reaction …

This article investigates the correlation between the Kappa and Lévy distributions via two
approaches of the Klein–Kramers equation. The first approach illustrates the velocity …

This article presents a local mesh-less procedure for simulating the Galilei invariant
fractional advection–diffusion (GI-FAD) equations in one, two, and three-dimensional …

Anomalous diffusion phenomena have been observed in many complex physical and
biological systems. One significant advance recently is the physical extension of particle's …