On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities

Saleh W., Meftah B., Awan M. U., LAKHDARI A.

Mathematics, vol.13, no.10, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 10
  • Publication Date: 2025
  • Doi Number: 10.3390/math13101575
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Hermite–Hadamard-type inequalities, Katugampola fractional multiplicative integrals, multiplicative s-convexity
  • Kocaeli University Affiliated: Yes

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.