The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey

By Francesco Mainardi, Antonio Mura, Gianni Pagnini. 2010

218 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7e20f28861af17b126f85212ec59687f420afa52

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In Applied Mathematics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Multivariate analogue of generalized Mittag-Leffler function (2011, background): “[21], Gorenflo and Luchko [7], Gorenflo and Mainardi [8], and a recent monograph published by Mainardi [20].”
FRACTIONAL CALCULUS AND WAVES IN LINEAR VISCOELASTICITY (2012, background): “The last reference would read: [Mainardi et al. (2010)] - p. 262, Bibliography.”
On a new class of abstract impulsive functional differential equations of fractional order (2014, background): “For a nice introduction, we refer to the reader to [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] and references cited therein.”
Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, methodology): “In [34] for instance, a solution of this equation was given as”