IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i13p1484-d581312.html
   My bibliography  Save this article

Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator

Author

Listed:
  • Azamat Dzarakhohov

    (Department of Mathematics and Physics, Gorsky State Agrarian University, Kirov Str. 37, North Ossetia-Alania, 362040 Vladikavkaz, Russia)

  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany)

  • Elina Shishkina

    (Department of Mathematical and Applied Analysis, Voronezh State University, Universitetskaya pl., 1, 394018 Voronezh, Russia
    Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy Street, 85, 308015 Belgorod, Russia)

Abstract

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.

Suggested Citation

  • Azamat Dzarakhohov & Yuri Luchko & Elina Shishkina, 2021. "Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator," Mathematics, MDPI, vol. 9(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1484-:d:581312
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/13/1484/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/13/1484/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elina Shishkina & Sergey Sitnik, 2019. "A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    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. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
    2. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

    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. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2024. "Time–space fractional Euler–Poisson–Darboux equation with Bessel fractional derivative in infinite and finite domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 383-402.

    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:gam:jmathe:v:9:y:2021:i:13:p:1484-:d:581312. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.