Trapezoidal and Midpoint-type Inequalities Based on Extended Conformable Operators (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we are explore some inequalities derived from twice differentiable functions together with the extended conformable fractional operators. First, we investigate two lemmas using extended conformable fractional operators. Then, we utilize these results to explore some new trapezoidal and midpoint-type inequalities through the use of the convex property of twice differentiable functions. Moreover, using the power mean inequality and H\"older's inequality, we introduce a new class of inequalities. The explored results are validated through different 2D and 3D graphs. This new class extends the results of previous research studies. The present paper seeks to motivate researchers to apply these concepts to other fractional operators.
Keywords: Extended conformable fractional operators; Trapezoidal-type inequalities; Midpoint-type inequalities; H\"older's inequality; Power mean inequality