We report on decay problem of classical systems. Mesoscopic level consideration is given on the basis of transient dynamics of non-interacting classical particles bounded in billiards. Three distinct decay channels are distinguished through the long-tailed memory effects revealed by temporal...

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e., D˜(r,t)=D(t)r−η with D(t)=Dδ(t)+D¯(t). The equation is considered in a confined region and subjected to time dependent...

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of...

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the N-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α). The presence...

We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (q-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic...

Exact solutions are rare for non-Markovian random walk models even in 1D, and much more so in 2D. Here we propose a 2D genuinely non-Markovian random walk model with a very rich phase diagram, such that the motion in each dimension can belong to one of 3 categories: (i) subdiffusive, (ii)...