Development of Fractional Newton-Type Inequalities Through Extended Integral Operators
Küçük Resim Yok
Tarih
2025
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann-Liouville (FR-L) operators, which forms the basis for deriving various inequalities under different assumptions on the integrand. In particular, fractional counterparts of the classical 1/3 and 3/8 Simpson rules are obtained when the modulus of the first derivative is convex. The analysis is further extended to include functions that satisfy a Lipschitz condition or have bounded first derivatives. Moreover, an additional NTI is presented for functions of bounded variation, expressed in terms of their total variation. In all scenarios, the proposed results reduce to classical inequalities when the fractional parameters are specified accordingly, thus offering a unified perspective on numerical integration through fractional operators.
Açıklama
Anahtar Kelimeler
Newton-type inequalities, generalized fractional operators, well-behaved functions
Kaynak
Fractaland Fractional
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
9
Sayı
7
