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On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities
1
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi Arabia
2
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
3
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
4
Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, Türkiye
5
Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(10), 1575; https://doi.org/10.3390/math13101575 (registering DOI)
Submission received: 11 April 2025
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Revised: 3 May 2025
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Accepted: 9 May 2025
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Published: 10 May 2025
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.
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MDPI and ACS Style
Saleh, W.; Meftah, B.; Awan, M.U.; Lakhdari, A.
On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities. Mathematics 2025, 13, 1575.
https://doi.org/10.3390/math13101575
AMA Style
Saleh W, Meftah B, Awan MU, Lakhdari A.
On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities. Mathematics. 2025; 13(10):1575.
https://doi.org/10.3390/math13101575
Chicago/Turabian Style
Saleh, Wedad, Badreddine Meftah, Muhammad Uzair Awan, and Abdelghani Lakhdari.
2025. "On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities" Mathematics 13, no. 10: 1575.
https://doi.org/10.3390/math13101575
APA Style
Saleh, W., Meftah, B., Awan, M. U., & Lakhdari, A.
(2025). On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities. Mathematics, 13(10), 1575.
https://doi.org/10.3390/math13101575
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