Jarunee SoontharanonMuhammad Aamir AliShahram RezapourMuhammad ToseefThanin Sitthiwirattham2025-03-102025-03-102025Sahand Communications in Mathematical Analysis2322580710.22130/scma.2024.2036770.18262-s2.0-85213877836https://repository.dusit.ac.th//handle/123456789/4440The main objective of this paper is to establish some new inequalities related to the open Newton-Cotes formulas in the setting of q-calculus. We establish a quantum integral identity first and then prove the desired inequalities for q-differentiable convex functions. These inequalities are useful for determining error bounds for the open Newton-Cotes formulas in both classical and q-calculus. This work distinguishes itself from existing studies by employing quantum operators, leading to sharper and more precise error estimates. These results extend the applicability of Newton-Cotes methods to quantum calculus, offering a novel contribution to the numerical analysis of convex functions. Finally, we provide mathematical examples and computational analysis to validate the newly established inequalities. © 2025 University of Maragheh. All rights reserved.Convex FunctionsFractional inequalitiesOpen Newton-Cotes Formulasq-CalculusArticleScopus