Better Approximation of Integral Form of Midpoint Formula Using p ‐Convex Function via Katugampola Fractional Integrals

In this article, new estimations of the integral form of the midpoint formula are derived for p ‐convex functions via Katugampola fractional integrals. A specific identity for differentiable functions is established, which extends and strengthens the integral midpoint inequality through innovative estimations. Moreover, estimations of the integral form of the midpoint formula are developed for functions whose first derivatives in absolute value are p ‐convex, employing Katugampola fractional integrals. Examples with graphs are presented to validate the results, and a comparison with previous findings demonstrates the superiority of the newly obtained inequalities.