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Article

A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability

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Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy
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Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
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Author to whom correspondence should be addressed.
Mathematics 2018, 6(1), 4; https://doi.org/10.3390/math6010004
Received: 18 November 2017 / Revised: 24 December 2017 / Accepted: 26 December 2017 / Published: 1 January 2018
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
In this paper, we show several connections between special functions arising from generalized Conway-Maxwell-Poisson (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. View Full-Text
Keywords: Hadamard fractional derivatives; COM-Poisson distributions; Modified Mittag–Leffler functions Hadamard fractional derivatives; COM-Poisson distributions; Modified Mittag–Leffler functions
MDPI and ACS Style

Garra, R.; Orsingher, E.; Polito, F. A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability. Mathematics 2018, 6, 4. https://doi.org/10.3390/math6010004

AMA Style

Garra R, Orsingher E, Polito F. A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability. Mathematics. 2018; 6(1):4. https://doi.org/10.3390/math6010004

Chicago/Turabian Style

Garra, Roberto, Enzo Orsingher, and Federico Polito. 2018. "A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability" Mathematics 6, no. 1: 4. https://doi.org/10.3390/math6010004

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