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

LAKHDARI A., Saleh W.

Mathematics, cilt.13, sa.21, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 21
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/math13213426
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: G-calculus, GA-convex functions, GG-convex functions, Hermite–Hadamard inequality, multiplicative midpoint inequality, multiplicative Riemann–Liouville fractional integrals, multiplicative trapezium inequality
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.