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 …

After a short excursion from the discovery of Brownian motion to the Richardson" law of four
thirds" in turbulent diffusion, the article introduces the Lévy flight superdiffusion as a self …

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 …

We establish a connection between anomalous heat conduction and anomalous diffusion in
one-dimensional systems. It is shown that if the mean square of the displacement of the …

The fractional Laplacian operator−(− Δ) α∕ 2 appears in a wide class of physical systems,
including Lévy flights and stochastic interfaces. In this paper, we provide a discretized …

We discuss the first passage time problem in the semi-infinite interval, for homogeneous
stochastic Markov processes with Lévy stable jump length distributions λ (x)∼ ℓ α/| x| 1+ α …

A bistable toggle switch is a paradigmatic model in the field of biology. The dynamics of the
system induced by Gaussian noise has been intensively investigated, but Gaussian noise …

We present the analysis of the first passage time problem on a finite interval for the
generalized Wiener process that is driven by Lévy stable noises. The complexity of the first …

We consider a Lévy flyer of order α that starts from a point x 0 on an interval [O, L] with
absorbing boundaries. We find a closed-form expression for the average number of flights …

We solve the problem of first-passage time for run-and-tumble particles in one dimension.
Exact expression is derived for the mean first-passage time in the general case, considering …