Fractional Milne-type inequalities for twice differentiable functions for Riemann-Liouville fractional integrals

Haider W., Budak H., Shehzadi A.

ANALYSIS AND MATHEMATICAL PHYSICS, cilt.14, sa.6, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 6
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s13324-024-00980-5
  • Dergi Adı: ANALYSIS AND MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this research, we investigate the error bounds associated with Milne's formula, a well-known open Newton-Cotes approach, initially focused on differentiable convex functions within the frameworks of fractional calculus. Building on this work, we investigate fractional Milne-type inequalities, focusing on their application to the more refined class of twice-differentiable convex functions. This study effectively presents an identity involving twice differentiable functions and Riemann-Liouville fractional integrals. Using this newly established identity, we established error bounds for Milne's formula in fractional and classical calculus. This study emphasizes the significance of convexity principles and incorporates the use of the H & ouml;lder inequality in formulating novel inequalities. In addition, we present precise mathematical illustrations to showcase the accuracy of the recently established bounds for Milne's formula.