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• W2223688510 abstract "We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi et al. (2001)): the first equation considered here is obtained by adding an exponential differential (or shift) operator expressed in terms of the Riesz–Feller derivative. We prove that this produces a random component in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involving the Riesz-derivative, we obtain, as a solution, the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift. Finally, we show that an extension of the space-fractional diffusion equation, containing both the fractional shift operator and the Feller integral, is satisfied by the transition density of the process obtained by time-changing the stable process with an independent linear birth process with drift." @default.
• W2223688510 created "2016-06-24" @default.
• W2223688510 creator A5075977936 @default.
• W2223688510 date "2018-07-01" @default.
• W2223688510 modified "2023-09-26" @default.
• W2223688510 title "Fractional diffusion-type equations with exponential and logarithmic differential operators" @default.
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• W2223688510 doi "https://doi.org/10.1016/j.spa.2017.09.013" @default.
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