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

Roberto Garra; Enzo Orsingher; Federico Polito

doi:10.3390/math6010004

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arXiv · 1711.07016

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

Roberto Garra·Enzo Orsingher·Federico Polito

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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.

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Roberto Garra, Enzo Orsingher, Federico Polito. 2017-11-19. A note on Hadamard fractional differential equations with varying coefficients and their applications in probability. https://doi.org/10.3390/math6010004

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