Further Hermite-Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Li H., Meftah B., Saleh W., Xu H., Kilicman A., Lakhdari A.

FRACTAL AND FRACTIONAL, cilt.8, sa.6, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 6
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/fractalfract8060345
  • Dergi Adı: FRACTAL AND FRACTIONAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

This paper introduces new versions of Hermite-Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order beta approaches 1, in addition to the fractional integrals we examined.