Work

Development of Fractional Newton-Type Inequalities Through Extended Integral Operators

Year: 2025

Type: article

Abstract: 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.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9070443

Authors: Abd-Allah Hyder, Areej A. Almoneef, Mohamed A. Barakat, Hüseyin Budak, Özge Aktaş

Institutions: King Khalid University, Princess Nourah bint Abdulrahman University, University of Tabuk, Kocaeli Üniversitesi, Düzce Üniversitesi

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: Princess Nourah Bint Abdulrahman University, King Khalid University