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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
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    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.
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