New Approach of Fractional Integral Inequalities Involving Interval-Valued Mappings with Applications to Matrix Analysis (Contemporary Mathematics, 2025)
Convexity via fractional calculus is a widely accepted concept that has attracted considerable interest in the field of applied mathematics. The aim of this paper is to develop new types of fractional Hermite-Hadamard-Mercer inequalities related to the generalized k-fractional conformable integral operator within the framework of interval analysis. To highlight the applicability of the concepts covered in this study, several illustrative examples are presented. The ideas and methods presented in this study could serve as a foundation for further research in this area.
Keywords: Hermite-Hadamard inequality; convexity; HH's Mercer inequality; generalized fractional k-operator; interval-valued mapping