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

Author

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  • Roberto Garra

    (Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy)

  • Enzo Orsingher

    (Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, P. le A. Moro 5, 00185 Roma, Italy)

  • Federico Polito

    (Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy)

Abstract

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.

Suggested Citation

  • Roberto Garra & Enzo Orsingher & Federico Polito, 2018. "A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability," Mathematics, MDPI, vol. 6(1), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:1:p:4-:d:124966
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
    2. Subrata Chakraborty & S. H. Ong, 2017. "Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    3. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    4. Beghin, Luisa & Macci, Claudio, 2017. "Asymptotic results for a multivariate version of the alternative fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 260-268.
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    Cited by:

    1. Ahmad Al-Omari & Hanan Al-Saadi, 2023. "( ω , ρ )-BVP Solution of Impulsive Hadamard Fractional Differential Equations," Mathematics, MDPI, vol. 11(20), pages 1-18, October.

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