Some new Boole's inequalities with respect to the middle ending point using k-conformable fractional integral operators via different classes of differentiable functions

Abstract

The objective of this study is to formulate a new definition of k-conformable fractional operators and to elucidate their boundedness and semigroup characteristics. Furthermore, we introduce an innovative identity for differentiable h-convex functions that employs k-conformable fractional operators.  By employing this identity, we have formulated novel inequalities applicable to bounded functions as well as Lipschitzian functions. In the subsequent section, we utilized h-convexity in conjunction with the power-mean inequality and Holder's inequality, respectively.