Work

Fractional Integral Estimates of Boole Type: Majorization and Convex Function Approach with Applications

Year: 2026

Type: article

Abstract: The goal of this paper is to use a Boole-type inequality framework to provide better estimates for differentiable functions. Using majorization theory, fractional integral operators are incorporated into a new auxiliary identity. The method establishes sharp bounds by combining the properties of convex functions with classical inequalities like the Power mean and Hölder inequalities, as well as the Niezgoda–Jensen–Mercer (NJM) inequality for majorized tuples. Additionally, the study presents real-world examples involving special functions and examines pertinent quadrature rules. This work’s primary contribution is the extension and generalization of a number of results that are already known in the current body of mathematical literature.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10010049

Authors: Saad Ihsan Butt, Mohammed Alammar, Youngsoo Seol

Institutions: COMSATS University Islamabad, Shaqra University, Dong-A University

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: National Research Foundation, Dong-A University, National Research Foundation of Korea