On Fractional Simpson-Type Inequalities via Harmonic Convexity

Li Liao, Abdelghani Lakhdari, Hongyan Xu and Badreddine Meftah ()
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Li Liao: School of Mathematical and Computer Science, Yichun University, Yichun 336000, China
Abdelghani Lakhdari: Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, Türkiye
Hongyan Xu: School of Mathematics and Physics, Suqian University, Suqian 223800, China
Badreddine Meftah: Laboratory of Analysis and Control of Differential Equations “ACED”, Department of Mathematics, Faculty MISM, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria

Mathematics, 2025, vol. 13, issue 23, 1-15

Abstract: In this paper, we establish some Simpson-type inequalities within the framework of Riemann–Liouville fractional calculus, specifically tailored for differentiable harmonically convex functions. By introducing a novel fractional integral identity for differentiable functions with harmonic arguments, we derive several estimates that generalize and refine existing results in the literature. The theoretical findings are validated through a numerical example supported by graphical illustration, and potential applications in approximation theory and numerical analysis are discussed.

Keywords: Riemann-Liouville fractional integrals; Simpson-type inequality; harmonically convex functions; Hölder’s inequality; power mean inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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