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

Abstract

Abstract New ways for comparing and bounding strongly ( s , m ) $(s,m)$ -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 ) $(s,m)$ -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.

Keywords

• Convex function
• s-convex function
• m-convex function
• Strongly convex function
• Hermite-Hadamard inequality
• Caputo-Fabrizio fractional integrals