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We consider some fractional extensions of the recursive differential equation governing the Pois-son process, i.e. d d t p k (t) = −λ(p k (t) − p k−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 " E k α,β (x), x ∈ (introduced by Prabhakar [24]) arise(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)
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)
We consider a fractional version of the classical non-linear birth process of which the Yule-Furry 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)
We analyse the vector process (X 0 (t), X 1 (t),. .. , Xn(t), t > 0) where X k (t) = t 0 X k−1 (s)ds, k = 1,. .. , n, and X 0 (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 (X 0 (t), X 1 (t), X 2 (t),(More)
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