Novel Fractional Simpson–Mercer-Type Inequalities and Their Applications

Arslan Munir, Hüseyin Budak, Artion Kashuri, Mohammed Rabih, Fatih Hezenci and Muhammad Muawwaz

Journal of Mathematics, 2026, vol. 2026, 1-16

Abstract: In this paper, we establish a Mercer-type identity for the Riemann–Liouville fractional integral. By using this identity, we derive several fractional Simpson–Mercer-type inequalities for functions whose third derivatives satisfy convexity-type assumptions in absolute value. Related estimates are also obtained under boundedness and Lipschitz continuity assumptions on the third derivative. Several known Simpson-type inequalities are recovered as special cases of the main results. To illustrate the effectiveness of the proposed results, numerical examples are provided. Furthermore, applications to Simpson-type quadrature formulas and the q-digamma function are discussed.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7179835

DOI: 10.1155/jom/7179835

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