Abstract
Based on the [Formula: see text]-shifting operator, we introduce the concept of Riemann–Liouville fractional quantum integration for interval-valued functions (IVFs), and establish new Riemann–Liouville fractional [Formula: see text]-Hermite–Hadamard ([Formula: see text]-HH) and [Formula: see text]-HH-Fejér inequalities for left and right [Formula: see text]-convex IVFs (LR-[Formula: see text]-convex-IVFs). The findings obtained generalize known results in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and fractional quantum calculus. The results are illustrated with examples.
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