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In this paper, we establish some Simpson-type inequalities within the framework of Riemann–Liouville fractional calculus, specifically tailored for differentiable harmonically convex functions. By introducing a novel fractional integral identity for differentiable functions with harmonic arguments, we derive several estimates that generalize and refine existing results in the literature. The theoretical findings are validated through a numerical example supported by graphical illustration, and potential applications in approximation theory and numerical analysis are discussed.
Liao et al. (Tue,) studied this question.