Demir, IzzettinTunc, Tuba2024-08-232024-08-2320240170-42141099-1476https://doi.org/10.1002/mma.10316https://hdl.handle.net/20.500.12684/14576In 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.en10.1002/mma.10316info:eu-repo/semantics/closedAccessconvex functionsproportional Caputo-hybrid operatorSimpson-type inequalitiesArticle2-s2.0-85197902681WOS:001262231100001Q1N/A