Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion...

We discuss the role of the initial conditions for the dynamical anomalies observed in the quasi-stationary states of the Hamiltonian mean field (HMF) model.

In recent years the interest around the study of anomalous relaxation and diffusion processes is increased due to their importance in several natural phenomena. Moreover, a further generalization has been developed by introducing time-fractional differentiation of distributed order which ranges...

A model, which describes contaminant transport in statistically homogeneous, disordered medium with sharply contrasting properties, is analyzed. At intermediate times, when there is no equilibrium between mobile and immobile contaminant fractions, the transport is described by a set of regimes...

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that...

We analyze a multidimensional nonlinear diffusion equation taking a spatial time dependent diffusion coefficient and external forces into account. We obtain new exact classes of solutions and investigate the transverse effects induced by an external force applied in the system. We also connect...

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return...

Moving particles that rest along their trajectory lead to time-fractional diffusion equations for the scaling limit distributions. For power law waiting times with infinite mean, the equation contains a fractional time derivative of order between 0 and 1. For finite mean waiting times, the most...

In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian...

The non-Markovian variant of the stochastic Liouville equation (SLE) based and the continuous time random walk approach (CTRWA) is proposed. This SLE turns out be represented by the conventional Markovian SLE. The non-Markovian SLE is applied to the analysis of anomalous long-tailed CTRW...