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On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities

Author

Listed:
  • 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
    Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria)

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.

Suggested Citation

  • Wedad Saleh & Badreddine Meftah & Muhammad Uzair Awan & Abdelghani Lakhdari, 2025. "On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities," Mathematics, MDPI, vol. 13(10), pages 1-34, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1575-:d:1653067
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    References listed on IDEAS

    as
    1. Muhammad Umar & Saad Ihsan Butt & Youngsoo Seol, 2025. "Hybrid Fractional Integral Inequalities In Multiplicative Calculus With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-28.
    2. Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Yu Peng & Tingsong Du, 2024. "ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-32.
    4. Zhou, Ziyi & Du, Tingsong, 2024. "Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    Full references (including those not matched with items on IDEAS)

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