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

By Roberto Garra, Enzo Orsingher, Federico Polito. 2017

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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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/b19eff8b4bd74d3c30086f29fb56a11b497fca95