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Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

Author

Listed:
  • Ahmed A. El-Deeb

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt)

  • Jan Awrejcewicz

    (Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland)

Abstract

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the ( γ , a ) -nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case.

Suggested Citation

  • Ahmed A. El-Deeb & Jan Awrejcewicz, 2021. "Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications," Mathematics, MDPI, vol. 9(22), pages 1-31, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2964-:d:683874
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    References listed on IDEAS

    as
    1. Young-Ho Kim, 2001. "An improvement of some inequalities similar to Hilbert's inequality," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 28, pages 1-11, January.
    2. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
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    Cited by:

    1. Ahmed A. El-Deeb & Samer D. Makharesh & Sameh S. Askar & Jan Awrejcewicz, 2022. "A Variety of Nabla Hardy’s Type Inequality on Time Scales," Mathematics, MDPI, vol. 10(5), pages 1-17, February.

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