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In this study, we focus on the newly introduced concept of LR-convex interval-valued functions to establish new variants of the Hermite–Hadamard (H-H) type and Pachpatte type inequalities for Riemann–Liouville fractional integrals. By presenting some numerical examples, we also verify the correctness of the results that we have derived in this paper. Because the results, which are related to the differintegral of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mrow><msub><mi>ϱ</mi><mn>1</mn></msub><mo>+</mo><msub><mi>ϱ</mi><mn>2</mn></msub></mrow><mn>2</mn></mfrac></semantics></math></inline-formula> type, are novel in the context of the LR-convex interval-valued functions, we believe that this will be a useful contribution for motivating future research in this area.