Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities

Abstract

Abstract In this article, firstly, Hermite–Hadamard’s inequality is generalized via a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. Then a new kernel is obtained and a new theorem valid for convex functions is proved for fractional order integrals. Also, some applications of our main findings are given.

Keywords

• Caputo–Fabrizio Fractional integral
• Convexity