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, cilt.2025, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1186/s13662-025-03976-y
  • Dergi Adı: Advances in Continuous and Discrete Models
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Convex functions, Fractional calculus, Maclaurin’s formula, Quadrature formulae
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.