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36 papers
The Mittag-Leffler function in the thinning theory for renewal processes
Rudolf Gorenflo, Francesco Mainardi
The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of po…
Operator theoretic approach to the Caputo derivative and the fractional diffusion equations
Rudolf Gorenflo, Yuri Luchko, Masahiro Yamamoto
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fracti…
Hilfer-Prabhakar Derivatives and Some Applications
Roberto Garra, Rudolf Gorenflo, Federico Polito +1
We present a generalization of Hilfer derivatives in which Riemann--Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties. Fur…
A Fractional Generalization of the Poisson Processes and Some of its Properties
Nicy Sebastian, Rudolf Gorenflo
We have provided a fractional generalization of the Poisson renewal processes by replacing the first time derivative in the relaxation equation of the survival probability by a fra…
Laplace-Laplace analysis of the fractional Poisson process
Rudolf Gorenflo, Francesco Mainardi
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace tra…
On the fractional Poisson process and the discretized stable subordinator
Rudolf Gorenflo, Francesco Mainardi
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation o…