Multiplicative Fractional Hermite–Hadamard-Type Inequalities in G-Calculus

LAKHDARI A., Saleh W.

Mathematics, vol.13, no.21, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 21
  • Publication Date: 2025
  • Doi Number: 10.3390/math13213426
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: G-calculus, GA-convex functions, GG-convex functions, Hermite–Hadamard inequality, multiplicative midpoint inequality, multiplicative Riemann–Liouville fractional integrals, multiplicative trapezium inequality
  • Kocaeli University Affiliated: Yes

Abstract

This paper extends Hermite–Hadamard-type inequalities to the fractional multiplicative framework of G-calculus. Using multiplicative Riemann–Liouville fractional integrals, we introduce a notion of multiplicative convexity and establish fractional Hermite–Hadamard, midpoint, and trapezoidal inequalities for (Formula presented.) -convex functions. Examples and graphical illustrations are provided to demonstrate the applicability of our results and further highlight the role of fractional multiplicative analysis in broadening traditional integral inequalities.