A Study on the New Class of Inequalities of Midpoint-Type and Trapezoidal-Type Based on Twice Differentiable Functions with Conformable Operators

Abstract

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder’s inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained.

On Conformable Fractional Milne-Type Inequalities

“…Hyder et al made significant contributions by introducing midpoint-type inequalities in [29]. In [30], Kara et al extended these efforts by providing midpoint-type and trapezoid-type inequalities specifically tailored for twice-differentiable convex functions.…”