Abstract In this paper, we establish generalized Simpson-type inequalities by conformable fractional integral operator. Utilizing functions with bounded second derivatives, we derive upper and lower bounds for these inequalities. This approach extends and generalizes existing results in the literature by providing more flexible conditions and broader applicability. Furthermore, we present special cases of the derived results to demonstrate their connection with existing inequalities in the literature. Numerical examples and graphical illustrations are provided to validate the theoretical findings and highlight the utility of the new operator. This study paves the way for further exploration in the field of fractional calculus and its applications in mathematical analysis and optimization.
Celik et al. (2026) studied this question.