On Fractional Simpson-Type Inequalities via Harmonic Convexity

Liao L., LAKHDARI A., Xu H., Meftah B.

Mathematics, cilt.13, sa.23, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 23
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/math13233778
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: harmonically convex functions, Hölder’s inequality, power mean inequality, Riemann-Liouville fractional integrals, Simpson-type inequality
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we establish some Simpson-type inequalities within the framework of Riemann–Liouville fractional calculus, specifically tailored for differentiable harmonically convex functions. By introducing a novel fractional integral identity for differentiable functions with harmonic arguments, we derive several estimates that generalize and refine existing results in the literature. The theoretical findings are validated through a numerical example supported by graphical illustration, and potential applications in approximation theory and numerical analysis are discussed.