Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type
are presented as a useful approach for the description of transport dynamics in complex …

Fractional dynamics has experienced a firm upswing during the past few years, having been
forged into a mature framework in the theory of stochastic processes. A large number of …

This chapter is devoted to time-and space-nonlocal generalizations of the standard Fourier
law, the corresponding generalizations of the classical heat conduction equation and …

Chaotic dynamics can be considered as a physical phenomenon that bridges the regular
evolution of systems with the random one. These two alternative states of physical …

We generalize the continuous time random walk (CTRW) to include the effect of space
dependent jump probabilities. When the mean waiting time diverges we derive a fractional …

In this Letter we introduce a generalization of the Lorenz dynamical system using fractional
derivatives. Thus, the system can have an effective noninteger dimension Σ defined as a …

We develop the finite element method for the numerical resolution of the space and time
fractional Fokker–Planck equation, which is an effective tool for describing a process with …

Recently, fractional calculus has attracted much attention since it plays an important role in
many fields of science and engineering. Especially, the study on stability of fractional …

We investigate fractional Brownian motion with a microscopic random-matrix model and
introduce a fractional Langevin equation. We use the latter to study both subdiffusion and …

Abstract Recently, Metzler et al.[Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional
Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the …