Sticky diffusion processes on bounded domains can spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on the boundary it can stay or move according to dynamics that are different from those in the interior. Such processes may be characterized by a...
Superdiffusion is a process in which diffusing molecules can make anomalously long jumps with relatively high probability. This process occurs, among others, in turbulent media and various biological processes related to cell migration. Superdiffusion is often described by the equation with the fractional Riesz derivative with respect to a spatial variable. This derivative is a...
In this talk we give an explicit solution to Dzherbashyan-Caputo-fractional Cauchy problems related to equations with derivatives of order $\nu_k$, for $k$ non-negative integer and $\nu > 0$. The solution is obtained by connecting the differential equation with the roots of the characteristic polynomial and it is expressed in terms of Mittag-Leffler-type functions. Under some additional...
