In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions.

A note on Hadamard fractional differential equations with varying coefficients and their applications in probability

Polito, Federico
2018-01-01

Abstract

In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions.
2018
6
1
1
10
https://arxiv.org/pdf/1711.07016
COM-Poisson distributions; Hadamard fractional derivatives; Modified Mittag- Leffler functions;
Garra, Roberto*; Orsingher, Enzo; Polito, Federico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1661277
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