A study of Hermite-Hadamard inequalities via Caputo-Fabrizio fractional integral operators using strongly (s,m)-convex functions in the second sense

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 17 - 24
• Main Authors: Li, Jie, Lin, Yong, Özcan, Serap, Saleem, Muhammad Shoaib, Shah, Ahsan Fareed
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Calculus; Caputo-Fabrizio fractional integrals; Convex analysis; Convex function; Derivatives; Engineering; Fractional calculus; Hermite-Hadamard inequality; Inequalities; Integrals; m-convex function; Mathematicians; Mathematics; Mathematics and Statistics; Operators (mathematics); Optimization; Partial differential equations; Robotics; s-convex function; Strongly convex function; Viscoelasticity; Convex function; Hermite-Hadamard inequality; Caputo-Fabrizio fractional integrals; Strongly convex function
• ISSN: 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03266-x

New ways for comparing and bounding strongly ( s , m ) -convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly ( s , m ) -convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.