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Two unified families of bivariate Mittag-Leffler functions

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  • Kürt, Cemaliye
  • Fernandez, Arran
  • Özarslan, Mehmet Ali

Abstract

The various bivariate Mittag-Leffler functions existing in the literature are gathered here into two broad families. Several different functions have been proposed in recent years as bivariate versions of the classical Mittag-Leffler function; we seek to unify this field of research by putting a clear structure on it. We use our general bivariate Mittag-Leffler functions to define fractional integral operators (which have a semigroup property) and corresponding fractional derivative operators (which act as left inverses and analytic continuations). We also demonstrate how these functions and operators arise naturally from some fractional partial integro-differential equations of Riemann–Liouville type.

Suggested Citation

  • Kürt, Cemaliye & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "Two unified families of bivariate Mittag-Leffler functions," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008530
    DOI: 10.1016/j.amc.2022.127785
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    References listed on IDEAS

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    1. Huseynov, Ismail T. & Ahmadova, Arzu & Fernandez, Arran & Mahmudov, Nazim I., 2021. "Explicit analytical solutions of incommensurate fractional differential equation systems," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. R. K. Saxena & S. L. Kalla, 2005. "Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-16, January.
    3. Yuri Luchko, 2020. "The Four-Parameters Wright Function of the Second kind and its Applications in FC," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
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    Cited by:

    1. Isah, Sunday Simon & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "On bivariate fractional calculus with general univariate analytic kernels," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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