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New Results Involving the Generalized Krätzel Function with Application to the Fractional Kinetic Equations

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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)

  • Rekha Srivastava

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

Abstract

Sun is a basic component of the natural environment and kinetic equations are important mathematical models to assess the rate of change of chemical composition of a star such as the sun. In this article, a new fractional kinetic equation is formulated and solved using generalized Krätzel integrals because the nuclear reaction rate in astrophysics is represented in terms of these integrals. Furthermore, new identities involving Fox–Wright function are discussed and used to simplify the results. We compute new fractional calculus formulae involving the Krätzel function by using Kiryakova’s fractional integral and derivative operators which led to several new identities for a variety of other classic fractional transforms. A number of new identities for the generalized Krätzel function are then analyzed in relation to the H -function. The closed form of such results is also expressible in terms of Mittag-Leffler function. Distributional representation of Krätzel function and its Laplace transform has been essential in achieving the goals of this work.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1060-:d:1074545
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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. Virginia Kiryakova, 2020. "Unified Approach to Fractional Calculus Images of Special Functions—A Survey," Mathematics, MDPI, vol. 8(12), pages 1-35, December.
    5. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
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