Work

On Proportional Caputo-Hybrid Fractional Milne-Type Inequalities: Theory, Numerical Simulations, and Applications

Year: 2026

Type: article

Abstract: The goal of this study is to establish a new type of Milne-type inequality in the scope of fractional calculus with the aid of proportional Caputo-hybrid operators. We will focus on two different scopes of regularity, which contain functions whose first and second derivatives are convex, and functions whose first and second derivatives are Lipschitz continuous. We will base these estimates on a new integral identity of proportional Caputo-hybrid integrals. We will show that the smoothness of the derivative influences the shape of the bounds. Convexity will cause symmetry. Lipschitz continuity will contain bounds on the modulus of continuity. To show that our results are accurate and easy to obtain, we included a full numerical example with graphics and applications to quadrature error estimation.

Source: Axioms

DOI: 10.3390/axioms15040280

Authors: Mariem Al-Hazmy, Yazeed Alkhrijah, Wedad Saleh, Borhen Louhichi, Badreddine Meftah

Institutions: Taibah University, Imam Mohammad ibn Saud Islamic University, University of Guelma

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Al-Imam Muhammad Ibn Saud Islamic University