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A Variety of Nabla Hardy’s Type Inequality on Time Scales

Author

Listed:
  • Ahmed A. El-Deeb

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

  • Samer D. Makharesh

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

  • Sameh S. Askar

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Jan Awrejcewicz

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

Abstract

The primary goal of this research is to prove some new Hardy-type ∇-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and ( γ , a ) -nabla Hölder inequality on time scales. The inequalities proved here extend and generalize existing results in the literature. Further, in the case when γ = 1 , we obtain some well-known time scale inequalities due to Hardy inequalities. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional h -sum inequalities, new conformable fractional q -sum inequalities and new classical conformable fractional integral inequalities.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:722-:d:757903
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    References listed on IDEAS

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    1. 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.
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