Modified Inequalities on Center-Radius Order Interval-Valued Functions Pertaining to Riemann–Liouville Fractional Integrals

Abstract

In this paper, we shall discuss a newly introduced concept of center-radius total-ordered relations between two intervals. Here, we address the Hermite–Hadamard-, Fejér- and Pachpatte-type inequalities by considering interval-valued Riemann–Liouville fractional integrals. Interval-valued fractional inequalities for a new class of preinvexity, i.e., cr-h-preinvexity, are estimated. The fractional operator is used for the first time to prove such inequalities involving center–radius-ordered functions. Some numerical examples are also provided to validate the presented inequalities.

Keywords

• interval-valued functions
• Hermite–Hadamard inequalities
• center–radius order
• Riemann–Liouville fractional operator