IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3372-d1208592.html
   My bibliography  Save this article

Distributional Representation of a Special Fox–Wright Function with an Application

Author

Listed:
  • Asifa Tassaddiq

    (Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada)

  • Ruhaila Md Kasmani

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Dalal Khalid Almutairi

    (Department of Mathematics, College of Education, Majmaah University, Al Majmaah 11952, Saudi Arabia)

Abstract

A review of the literature demonstrates that the Fox–Wright function is not only a mathematical puzzle, but its role is naturally to represent basic physical phenomena. Motivated by this fact, we studied a new representation of this function in terms of complex delta functions. This representation was useful to compute its Laplace transform with respect to the third parameter γ for which it also generalizes the one and two-parameter Mittag-Leffler functions. New identities involving the Fox–Wright function were discussed and used to simplify the results. Different fractional transforms were evaluated and the solution of a fractional kinetic equation was obtained by using its new representation. Several new properties of this function were discussed as a distribution.

Suggested Citation

  • Asifa Tassaddiq & Rekha Srivastava & Ruhaila Md Kasmani & Dalal Khalid Almutairi, 2023. "Distributional Representation of a Special Fox–Wright Function with an Application," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3372-:d:1208592
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3372/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/15/3372/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. Aslam Chaudhry & Asghar Qadir, 2004. "Fourier transform and distributional representation of the gamma function leading to some new identities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-6, January.
    2. Virginia Kiryakova, 2020. "Unified Approach to Fractional Calculus Images of Special Functions—A Survey," Mathematics, MDPI, vol. 8(12), pages 1-35, December.
    Full references (including those not matched with items on IDEAS)

    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. Asifa Tassaddiq & Rekha Srivastava, 2023. "New Results Involving the Generalized Krätzel Function with Application to the Fractional Kinetic Equations," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    2. Asifa Tassaddiq, 2019. "A New Representation of the k-Gamma Functions," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    3. Asifa Tassaddiq, 2020. "A New Representation of the Generalized Krätzel Function," Mathematics, MDPI, vol. 8(11), pages 1-17, November.

    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:11:y:2023:i:15:p:3372-:d:1208592. 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.