On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities
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...
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MDPI AG
2025-05-01
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| Online Access: | https://www.mdpi.com/2227-7390/13/10/1575 |
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| author | Wedad Saleh Badreddine Meftah Muhammad Uzair Awan Abdelghani Lakhdari |
| author_facet | Wedad Saleh Badreddine Meftah Muhammad Uzair Awan Abdelghani Lakhdari |
| author_sort | Wedad Saleh |
| collection | DOAJ |
| description | 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 <i>s</i>-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 <i>s</i>-convex. These results extend classical integral inequalities to the multiplicative fractional calculus setting, offering enhanced precision in approximating nonlinear phenomena. |
| format | Article |
| id | doaj-art-3aa964ed85ef4dafafe890b11c033b2c |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-3aa964ed85ef4dafafe890b11c033b2c2025-08-20T01:56:31ZengMDPI AGMathematics2227-73902025-05-011310157510.3390/math13101575On Katugampola Fractional Multiplicative Hermite-Hadamard-Type InequalitiesWedad Saleh0Badreddine Meftah1Muhammad Uzair Awan2Abdelghani Lakhdari3Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi ArabiaLaboratory 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, AlgeriaDepartment of Mathematics, Government College University, Faisalabad 38000, PakistanDepartment of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, TürkiyeThis 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 <i>s</i>-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 <i>s</i>-convex. These results extend classical integral inequalities to the multiplicative fractional calculus setting, offering enhanced precision in approximating nonlinear phenomena.https://www.mdpi.com/2227-7390/13/10/1575Katugampola fractional multiplicative integralsHermite–Hadamard-type inequalitiesmultiplicative s-convexity |
| spellingShingle | Wedad Saleh Badreddine Meftah Muhammad Uzair Awan Abdelghani Lakhdari On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities Mathematics Katugampola fractional multiplicative integrals Hermite–Hadamard-type inequalities multiplicative s-convexity |
| title | On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities |
| title_full | On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities |
| title_fullStr | On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities |
| title_full_unstemmed | On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities |
| title_short | On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities |
| title_sort | on katugampola fractional multiplicative hermite hadamard type inequalities |
| topic | Katugampola fractional multiplicative integrals Hermite–Hadamard-type inequalities multiplicative s-convexity |
| url | https://www.mdpi.com/2227-7390/13/10/1575 |
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