相关论文: Retarding Sub- and Accelerating Super-Diffusion Go…

The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…

We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules…

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its…

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…

We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…

The fractional diffusion-wave equation (FDWE) is a recent generalization of diffusion and wave equations via time and space fractional derivatives. The equation underlies Levy random walk and fractional Brownian motion and is foremost…

Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…

In this paper, we aim to explore optimal regional trajectory tracking control problems of the anomalous subdiffusion processes governed by time-fractional diffusion systems under the Neumann boundary conditions. Using eigenvalue theory of…

In slowly evolving spherical potentials, $\Phi(r,t)$, radial actions are typically assumed to remain constant. Here, we construct dynamical invariants that allow us to derive the evolution of radial actions in spherical central potentials…

The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…

Based on the Langevin description of the Continuous Time Random Walk (CTRW), we consider a generalization of CTRW in which the waiting times between the subsequent jumps are correlated. We discuss the cases of exponential and slowly…

Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately…

The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…

We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…

Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…

It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…