In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as -Wright function, entering as a probability density in arelevant class of self-similar stochastic processes that we generally refer to as time-fractionaldiffusion processes. Indeed, the master equations governing these processesgeneralize the standard diffusion equation by means of time-integral operators interpretedas derivatives of fractional order. When these generalized diffusion processes are properlycharacterized with stationary increments, the -Wright function is shown to play thesame key role as the Gaussian density in the standard and fractional Brownian motions.Furthermore, these processes provide stochastic models suitable for describing phenomenaof anomalous diffusion of both slow and fast types.
"The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey." Int. J. Differ. Equ. 2010 (SI1) 1 - 29, 2010. https://doi.org/10.1155/2010/104505