Enzo Orsingher

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We consider some fractional extensions of the recursive differential equation governing the Poisson process, i.e. d d t pk(t) =−λ(pk(t)− pk−1(t)), k ≥ 0, t > 0 by introducing fractional time-derivatives of order ν , 2ν , ..., nν . We show that the so-called “Generalized Mittag-Leffler functions” Ek α,β(x), x ∈ R (introduced by Prabhakar [24]) arise as(More)
In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X (t), t ≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration(More)
We consider a fractional version of the classical non-linear birth process of which the YuleFurry model is a particular case. Fractionality is obtained by replacing the first-order time derivative in the difference-differential equations which govern the probability law of the process, with the Dzherbashyan-Caputo fractional derivative. We derive the(More)
In this paper we discuss some explicit results related to the fractional Klein-Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein-Gordon equation to a case of fractional hyper-Bessel equation. We find an explicit analytical solution by using the McBride theory of(More)
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