On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities

Wedad Saleh, Badreddine Meftah (), Muhammad Uzair Awan () and Abdelghani Lakhdari
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Wedad Saleh: Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi Arabia
Badreddine Meftah: Laboratory of Analysis and Control of Differential Equations “ACED”, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria
Muhammad Uzair Awan: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Abdelghani Lakhdari: Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, Türkiye

Mathematics, 2025, vol. 13, issue 10, 1-34

Abstract: This paper presents a novel framework for Katugampola fractional multiplicative integrals, advancing recent breakthroughs in fractional calculus through a synergistic integration of multiplicative analysis. Motivated by the growing interest in fractional calculus and its applications, we address the gap in generalized inequalities for multiplicative s -convex functions by deriving a Hermite–Hadamard-type inequality tailored to Katugampola fractional multiplicative integrals. A cornerstone of our work involves the derivation of two groundbreaking identities, which serve as the foundation for midpoint- and trapezoid-type inequalities designed explicitly for mappings whose multiplicative derivatives are multiplicative s -convex. These results extend classical integral inequalities to the multiplicative fractional calculus setting, offering enhanced precision in approximating nonlinear phenomena.

Keywords: Katugampola fractional multiplicative integrals; Hermite–Hadamard-type inequalities; multiplicative s -convexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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