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We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is constructed by considering the difference-differential equation governing the distribution of the standard Poisson process, N(t), t > 0, and by replacing the… (More)

- Enzo Orsingher
- 2010

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)

- Alexander I. Zeifman, S. Leorato, Enzo Orsingher, Yacov Satin, Galina Shilova
- Queueing Syst.
- 2006

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)

The telegrapher’s process with drift is here examined and its distribution is obtained by applying the Lorentz transformation. The related characteristic function as well as the distribution are also derived by solving an initial value problem for the generalized telegraph equation.

- Enzo Orsingher, Bruno Toaldo
- J. Applied Probability
- 2015

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)

- Roberto Garra, Federico Polito, Enzo Orsingher
- ICFDA'14 International Conference on Fractional…
- 2014

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)

- Enzo Orsingher
- 2002

We analyse the vector process (X0(t), X1(t), . . . , Xn(t), t > 0) where Xk(t) = t ∫ 0 Xk−1(s)ds, k = 1, . . . , n, and X0(t) is the two-valued telegraph process. In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed. Special care is given to the case of the process (X0(t), X1(t), X2(t), t > 0)… (More)

- Roberto Garra, Enzo Orsingher, Federico Polito
- J. Applied Probability
- 2015

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