Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

Abstract

In this paper, we aim to discuss some fractional Hermite-Hadamard (H-H)-Mercer inequality for interval-valued functions via generalized fractional integral operator (GFIO). In addition, we investigate some new variants of the H-H-Mercer inequality pertaining to GFIO. A few examples are also provided to back up our claims. The findings potentially shed fresh light on a wide range of integral inequalities for fractional fuzzy in the frame of interval analysis and the optimization challenges they present. Finally, applications involving matrices are demonstrated.