Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives

Abstract

In this article, certain Hermite–Jensen–Mercer type inequalitie s are proved via Caputo fractional derivatives. We established some new inequalities involving Caputo fractional derivatives, such as Hermite–Jensen–Mercer type inequalities, for differentiable mapping <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msup></mml:mrow></mml:math> whose derivatives in the absolute values are convex.