Fractional Milne-type inequalities for twice differentiable functions for Riemann-Liouville fractional integrals
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Basel Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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.
Açıklama
Anahtar Kelimeler
Inequalities of Milne-type, Fractional version, Twice differentiable convex function
Kaynak
Analysisand Mathematical Physics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
14
Sayı
6
