Related papers: Fractional Diffusion Equation for a Power-Law-Trun…
The L\'evy walk process for a lower interval of an excursion times distribution ($\alpha<1$) is discussed. The particle rests between the jumps and the waiting time is position-dependent. Two cases are considered: a rising and diminishing…
Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…
We introduce a formalism of fractional diffusion on networks based on a fractional Laplacian matrix that can be constructed directly from the eigenvalues and eigenvectors of the Laplacian matrix. This fractional approach allows random walks…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --L\'evy-type distribution. Based on recent predictions made for 1D…
The method of approximate automodel solution for the Green's function of the time-dependent superdiffusive (nonlocal) transport equations (J. Phys. A: Math. Theor. 49 (2016) 255002) is extended to the case of a finite velocity of carriers.…
We report on the distribution spectra of the fluctations in the amount of power injected into a liquid crystal undergoing electroconvective flow. The probability distribution functions (PDFs) of the fluctuations as well as the magnitude of…
We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficient,…
L\'{e}vy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the L\'{e}vy walk with the exponent of the power-law distributed flight time $\alpha\in(0,2)$. We…
Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where upon resetting the particle is…
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
We have provided a fractional generalization of the Poisson renewal processes by replacing the first time derivative in the relaxation equation of the survival probability by a fractional derivative of order $\alpha ~(0 < \alpha \leq 1)$. A…
We study a turbulence closure model in which the fractional Laplacian $(-\Delta)^\alpha$ of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of the model by applying Pao's energy transfer theory.…
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes…
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the…