Thanin SitthiwiratthamMuhammad Aamir AliHüseyin BudakChanon Promsakon2025-07-072025-07-072025Rocky Mountain Journal of Mathematics35759610.1216/rmj.2025.55.2552-s2.0-105005882212https://repository.dusit.ac.th/handle/123456789/7312We establish error bounds for the open Newton–Cotes formula with n = 1 for differentiable convex functions in fractional calculus. We use for this purpose an integral identity, which we prove, having Riemann–Liouville fractional integral and ordinary derivative. We give applications for special means, and add an example to show the validity of inequalities with a graph for different values of fractional parameter α. © Rocky Mountain Mathematics Consortium.convex functionopen Newton–Cotes formulaArticleScopus