A new approach to Simpson‐type inequality with proportional Caputo‐hybrid operator

Abstract

In this article, we begin by deriving a new identity with the help of twice‐differentiable convex functions for the proportional Caputo‐hybrid operator. Then, using this newly uncovered identity, we obtain various integral inequalities associated with the Simpson's integral inequality for proportional Caputo‐hybrid operator. Moreover, we indicate that the acquired results improve and refine certain existing discoveries in the realm of integral inequalities. Finally, for a better understanding of the newly obtained inequalities, we establish illustrative examples and visualize them through their corresponding graphs.