HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL

Fractional [Formula: see text]-calculus is considered to be the fractional analogs of [Formula: see text]-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) [Formula: see text]-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving [Formula: see text]-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF [Formula: see text]-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.