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A New Representation of the Generalized Krätzel Function

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  • Asifa Tassaddiq

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

Abstract

The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these functions is formulated over a particular set of test functions. This is validated using the classical Fourier transform. The results lead to a novel extension of Krätzel functions by introducing distributions in terms of the delta function. A new version of the generalized Krätzel integral transform emerges as a natural consequence of this research. The relationship between the Krätzel function and the H -function is also explored to study new identities.

Suggested Citation

  • Asifa Tassaddiq, 2020. "A New Representation of the Generalized Krätzel Function," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2009-:d:443135
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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. G. L. N. Rao & L. Debnath, 1985. "A generalized Meijer transformation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-7, January.
    3. Al-Lail, Mohammed H. & Qadir, Asghar, 2015. "Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 392-397.
    4. Tassaddiq, Asifa, 2019. "MHD flow of a fractional second grade fluid over an inclined heated plate," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 341-346.
    5. Tassaddiq, Asifa & Khan, I. & Nisar, K.S., 2020. "Heat transfer analysis in sodium alginate based nanofluid using MoS2 nanoparticles: Atangana–Baleanu fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    Full references (including those not matched with items on IDEAS)

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