New approaches on fractional integral inequalities for functions whose higher-order derivatives are bounded

Erden S., Ozdemir B. G., YILDIZ Ç., Cotîrla L., Breaz D.

Demonstratio Mathematica, cilt.59, sa.1, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1515/dema-2025-0198
  • Dergi Adı: Demonstratio Mathematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Linguistic Bibliography, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Riemann-Liouville fractional integral operator, Ostrowski inequality, absolutely continuous functions, numerical integration
  • Atatürk Üniversitesi Adresli: Evet

Özet

In the present paper, utilizing a wide class of fractional integral operators (namely the Riemann-Liouville fractional integral operator) and some functions whose higher-order derivatives are absolutely continuous, we develop novel fractional integral inequalities of the Ostrowski type. Furthermore, the results obtained are found to correlate with the findings of previous studies which have identified inequalities. Finally, novel composite quadrature rules are investigated for estimating the remainder term of fractional integral of a function. In conclusion, the methodology described in this article is expected to stimulate further research in this area.