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Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule

Author

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  • 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)

  • Hasan Kara

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

  • Mehmet Zeki Sarikaya

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

Abstract

Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann–Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson’s inequalities is the first paper in the literature as a method.

Suggested Citation

  • Hüseyin Budak & Fatih Hezenci & Hasan Kara & Mehmet Zeki Sarikaya, 2023. "Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2282-:d:1146462
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    References listed on IDEAS

    as
    1. Miguel Vivas-Cortez & Thabet Abdeljawad & Pshtiwan Othman Mohammed & Yenny Rangel-Oliveros, 2020. "Simpson’s Integral Inequalities for Twice Differentiable Convex Functions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-15, June.
    2. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    3. Du, Tingsong & Li, Yujiao & Yang, Zhiqiao, 2017. "A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 358-369.
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