Work

Fractional Hermite–Hadamard and Bullen-Type Inequalities on the Discrete Time Scale

Year: 2026

Type: article

Abstract: This paper develops a unified fractional version of the Hermite–Hadamard inequality and Bullen-type inequalities for convex functions defined on discrete time scales. By employing generalized fractional difference operators, the obtained result encompasses and extends previously known discrete formulations, including both the classical case and higher-order variants. Furthermore, we investigate the approximation accuracy of the introduced fractional mean operator. Specifically, we establish explicit error bounds for Lipschitz functions and for functions with convex differences, providing a more comprehensive analysis of the discrete fractional setting.

Source: Mathematics

DOI: 10.3390/math14040598

Authors: Rubayyi T. Alqahtani, Mehmet Zeki Sarikaya

Institutions: Imam Mohammad ibn Saud Islamic University, Düzce Üniversitesi

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Al-Imam Muhammad Ibn Saud Islamic University