On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (<i>s</i>, <i>m</i>)-Convex Functions

Abstract

This paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Caputo–Fabrizio integral operators are derived for those functions whose derivatives are (s,m)-convex. Inequalities involving the digamma function and special means are deduced as applications.

Keywords

• (<i>s</i>, <i>m</i>)-convex function
• Hermite–Hadamard inequalities
• Caputo fractional derivative
• Caputo–Fabrizio integral operator