New Riemann-Liouville Fractional-Order Inclusions for Convex Functions via Interval-Valued Settings Associated with Pseudo-Order Relations

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 rho(1)+rho(2)/2 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.

Automated summary

This study introduces the concept of LR-convex interval-valued functions and establishes new variants of the Hermite-Hadamard (H-H) type and Pachpatte type inequalities for Riemann-Liouville fractional integrals. Numerical examples are provided to verify the correctness of the results. The novelty of these results, related to the differintegral of the rho(1)+rho(2)/2 type, in the context of LR-convex interval-valued functions, makes them a useful contribution for motivating future research in this area.