The M-Wright Function in Time-Fractional Diffusion Processes : A Tutorial Survey
Joint Authors
Pagnini, Gianni
Mura, Antonio
Mainardi, Francesco
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-29, 29 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-02-11
Country of Publication
Egypt
No. of Pages
29
Main Subjects
Abstract EN
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we generally refer to as time-fractional diffusion processes.
Indeed, the master equations governing these processes generalize the standard diffusion equation by means of time-integral operators interpreted as derivatives of fractional order.
When these generalized diffusion processes are properly characterized with stationary increments, the M-Wright function is shown to play the same key role as the Gaussian density in the standard and fractional Brownian motions.
Furthermore, these processes provide stochastic models suitable for describing phenomena of anomalous diffusion of both slow and fast types.
American Psychological Association (APA)
Mainardi, Francesco& Mura, Antonio& Pagnini, Gianni. 2010. The M-Wright Function in Time-Fractional Diffusion Processes : A Tutorial Survey. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-29.
https://search.emarefa.net/detail/BIM-446680
Modern Language Association (MLA)
Mainardi, Francesco…[et al.]. The M-Wright Function in Time-Fractional Diffusion Processes : A Tutorial Survey. International Journal of Differential Equations No. 2010 (2010), pp.1-29.
https://search.emarefa.net/detail/BIM-446680
American Medical Association (AMA)
Mainardi, Francesco& Mura, Antonio& Pagnini, Gianni. The M-Wright Function in Time-Fractional Diffusion Processes : A Tutorial Survey. International Journal of Differential Equations. 2010. Vol. 2010, no. 2010, pp.1-29.
https://search.emarefa.net/detail/BIM-446680
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446680