| Summary: | In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Hölder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">H</mi><mo>)</mo></mrow></semantics></math></inline-formula> type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.
|
|---|