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

Hüseyin Budak (), Fatih Hezenci, Hasan Kara and Mehmet Zeki Sarikaya
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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

Mathematics, 2023, vol. 11, issue 10, 1-16

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.

Keywords: Simpson-type inequality; integral inequalities; bounded functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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