Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion
Joint Authors
Pagnini, Gianni
Mura, Antonio
Mainardi, Francesco
Source
International Journal of Stochastic Analysis
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-16
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Pagnini, Gianni& Mura, Antonio& Mainardi, Francesco. 2012. Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion. International Journal of Stochastic Analysis،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-471371
Modern Language Association (MLA)
Pagnini, Gianni…[et al.]. Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion. International Journal of Stochastic Analysis No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-471371
American Medical Association (AMA)
Pagnini, Gianni& Mura, Antonio& Mainardi, Francesco. Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion. International Journal of Stochastic Analysis. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-471371
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-471371