Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for <i>h</i>-Convex Function

Abstract

Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function via a Caputo–Fabrizio fractional integral. We develop some novel Caputo–Fabrizio fractional integral inequalities. We also present Caputo–Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite–Jensen–Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.

Keywords

• convex function
• <i>h</i>-convex function
• Hermite–Hadamard inequality
• Caputo–Fabrizio fractional integral
• Hermite–Hadamard inequality
• Jensen inequality