Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion
type: Item
instance of: scholarly article
title: Generalized fractional master equation for self-similar stochastic processes modelling anomalous diffusion
zbMATH Open document ID: 1260.60163
DOI: 10.1155/2012/427383
author: Gianni Pagnini
author: Antonio Mura
author: Francesco Mainardi
published in: International Journal of Stochastic Analysis
publication date: 2013-01-09T00:00:00Z
review text: Summary: The master equation approach to model anomalous diffusion is considered. Anomalous diffusion in complex media can be described as the result of a superposition mechanism reflecting inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting master equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function) emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G18
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 6123592
zbMATH Keywords: master equation approach
zbMATH Keywords: anomalous diffusion in complex media
zbMATH Keywords: time-fractional diffusion process
zbMATH Keywords: grey Brownian motion
Wikidata QID: Q58689562
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/427383
OpenAlex ID: W2157358771
cites work: Q4264353
cites work: The Fokker-Planck equation. Methods of solution and applications.
cites work: Handbook of stochastic methods for physics, chemistry and the natural sciences.
cites work: Q4863397
cites work: Higher order fractional variational optimal control problems with delayed arguments
cites work: Fractional-order attractors synthesis via parameter switchings
cites work: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
cites work: Q2741107
cites work: Q4438501
cites work: Nonlinear time-fractional differential equations in combustion science
cites work: And I say to myself: “What a fractional world!”
cites work: Q3008210
cites work: Q4028304
cites work: A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics
cites work: Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
cites work: Erdélyi-Kober fractional diffusion
cites work: The fundamental solution of the space-time fractional diffusion equation
cites work: The \(M\)-Wright function in time-fractional diffusion processes: a tutorial survey
cites work: Q4282622
cites work: Q3421742
cites work: Q3533524
cites work: Q5190149
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
cites work: Q4438451
cites work: Wright functions as scale-invariant solutions of the diffusion-wave equation
Recommended article: Anomalous Diffusion: From Fractional Master Equations to Path Integrals
Recommended article: Generalized diffusion equation with fractional derivatives within Renyi statistics
Recommended article: On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
Recommended article: Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions
Recommended article: Fractional Diffusion Equations and Anomalous Diffusion
Recommended article: Generalized Continuous Time Random Walks, Master Equations, and Fractional Fokker--Planck Equations
Recommended article: Generalized master equations and fractional Fokker-Planck equations from continuous time random walks with arbitrary initial conditions
Recommended article: Dynamics of a stochastic fractional reaction-diffusion equation
Recommended article: On a fractional master equation
Recommended article: Solutions for a generalized fractional anomalous diffusion equation
description: scientific article; zbMATH DE number 6123592