IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v443y2023ics0096300322008530.html
   My bibliography  Save this article

Two unified families of bivariate Mittag-Leffler functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322008530
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127785?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Mahmudov, Nazim I. & Aydın, Mustafa, 2021. "Representation of solutions of nonhomogeneous conformable fractional delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008530. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.