Fractional Euler–Maclaurin-type inequalities for twice-differentiable functions

Shehzadi A., BUDAK H., Haider W., Hezenci F., Chen H.

Advances in Continuous and Discrete Models, vol.2025, no.1, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2025 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1186/s13662-025-03976-y
  • Journal Name: Advances in Continuous and Discrete Models
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Convex functions, Fractional calculus, Maclaurin’s formula, Quadrature formulae
  • Kocaeli University Affiliated: Yes

Abstract

This article establishes a novel equality for twice-differentiable functions with convex absolute values in their second derivatives. This equality is used to establish Euler–Maclaurin-type inequalities through Riemann–Liouville fractional integrals. By utilizing convexity, the power mean inequality, and the Hölder inequality, several significant fractional inequalities can be derived. Moreover, the recently derived inequalities are not only grounded in theory but are also accompanied by concrete instances to further solidify their validity.