Fractional Integral Inequalities of Riemann–Liouville Type for Higher-Order Differentiable Convex Mappings

Erden S., BUDAK H.

Mathematical Methods in the Applied Sciences, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1002/mma.70690
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: convex function, Hermite–Hadamard inequality, higher-order derivatives, Riemann–Liouville fractional integral
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher-order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right-hand side of the fundamental Hermite–Hadamard inequality to higher-order derivatives, along with its special cases. We also establish fractional inequalities for functions whose We also examined how fractional inequalities come out for functions whose higher-order derivatives, in absolute value, are convex. Lastly, we examine how to generalize the basic Hermite–Hadamard inequalities to fractional integral inequalities for functions whose derivatives of any order are convex. It is given which special case of this generalized integral yields the Hermite–Hadamard inequality.