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

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1002/mma.70690
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Keywords: convex function, Hermite–Hadamard inequality, higher-order derivatives, Riemann–Liouville fractional integral
  • Kocaeli University Affiliated: Yes

Abstract

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.