Open Access
2010 The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey
Francesco Mainardi, Antonio Mura, Gianni Pagnini
Int. J. Differ. Equ. 2010(SI1): 1-29 (2010). DOI: 10.1155/2010/104505


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.


Download Citation

Francesco Mainardi. Antonio Mura. Gianni Pagnini. "The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey." Int. J. Differ. Equ. 2010 (SI1) 1 - 29, 2010.


Received: 13 September 2009; Accepted: 8 November 2009; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1222.60060
MathSciNet: MR2592742
Digital Object Identifier: 10.1155/2010/104505

Rights: Copyright © 2010 Hindawi

Vol.2010 • No. SI1 • 2010
Back to Top