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Erdélyi-Kober fractional diffusion

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Abstract

The aim of this Short Note is to highlight that the generalized grey Brownian motion (ggBm) is an anomalous diffusion process driven by a fractional integral equation in the sense of Erdélyi-Kober, and for this reason here it is proposed to call such family of diffusive processes as Erdélyi-Kober fractional diffusion. The ggBm is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion. This class is made up of self-similar processes with stationary increments and it depends on two real parameters: 0 < α ≤ 2 and 0 < β ≤ 1. It includes the fractional Brownian motion when 0 < α ≤ 2 and β = 1, the time-fractional diffusion stochastic processes when 0 < α = β < 1, and the standard Brownian motion when α = β = 1. In the ggBm framework, the 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.

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  1. CRS4, Center for Advanced Studies, Research and Development in Sardinia, Polaris Bldg. 1, 09010, Pula, CA, Italy

    Gianni Pagnini

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  1. Gianni Pagnini
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Correspondence to Gianni Pagnini.

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Pagnini, G. Erdélyi-Kober fractional diffusion. fcaa 15, 117–127 (2012). https://doi.org/10.2478/s13540-012-0008-1

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  • DOI: https://doi.org/10.2478/s13540-012-0008-1

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