We analyze an anisotropic fractional diffusion equation that extends some known diffusion equations by considering a diffusion coefficient with spatial and time dependence, the presence of external forces and time fractional derivatives. We obtain new exact classes of solutions for a linear...

A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in...

We study the stochastic fractional diffusive limit of a kinetic equation involving a small parameter and perturbed by a smooth random term. Generalizing the method of perturbed test functions, under an appropriate scaling for the small parameter, and with the moment method used in the...

The fast increase in computing power makes it possible to rapidly generate synthetic high frequency financial time series by Monte Carlo with any desired distribution of the increments and of the waiting times between increments, even for sets of securities as large as those traded on a whole...

Time series models showing power law tails in autocorrelation functions are common in econometrics. A special non-Markovian model for such kind of time series is provided by the random walk introduced by Gorenflo et al. as a discretization of time fractional diffusion. The time series so...

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...