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New Extensions of the Parameterized Inequalities Based on Riemann–Liouville Fractional Integrals

Author

Listed:
  • Hasan Kara

    (Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye)

  • Fatih Hezenci

    (Department of Mathematics, Faculty of Science and Arts, Duzce University, Düzce 81620, Türkiye)

Abstract

In this article, we derive the above and below bounds for parameterized-type inequalities using the Riemann–Liouville fractional integral operators and limited second derivative mappings. These established inequalities generalized the midpoint-type, trapezoid-type, Simpson-type, and Bullen-type inequalities according to the specific choices of the parameter. Thus, a generalization of many inequalities and new results were obtained. Moreover, some examples of obtained inequalities are given for better understanding by the reader. Furthermore, the theoretical results are supported by graphs in order to illustrate the accuracy of each of the inequalities obtained according to the specific choices of the parameter.

Suggested Citation

  • Hasan Kara & Hüseyin Budak & Fatih Hezenci, 2022. "New Extensions of the Parameterized Inequalities Based on Riemann–Liouville Fractional Integrals," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3374-:d:917056
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    References listed on IDEAS

    as
    1. Tingsong Du & Chunyan Luo & Zhijie Cao, 2021. "On The Bullen-Type Inequalities Via Generalized Fractional Integrals And Their Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-20, November.
    2. A. Barani & S. Barani & S. S. Dragomir, 2012. "Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P -Convex," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, July.
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    Cited by:

    1. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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