Fractional Hermite–Hadamard–Mercer-Type Inequalities for Interval-Valued Convex Stochastic Processes with Center-Radius Order and Their Related Applications in Entropy and Information Theory.

We propose a new definition of the γ -convex stochastic processes (C SP) using center and radius (CR) order with the notion of interval valued functions (C. R I. V) . By utilizing this definition and Mean-Square Fractional Integrals, we generalize fractional Hermite–Hadamard–Mercer-type inclusions for generalized   C. R I. V versions of convex, tgs-convex, P-convex, exponential-type convex, Godunova–Levin convex, s-convex, Godunova–Levin s-convex, h-convex, n-polynomial convex, and fractional n-polynomial (C SP) . Also, our work uses interesting examples of   C. R I. V (C SP) with Python-programmed graphs to validate our findings using an extension of Mercer's inclusions with applications related to entropy and information theory. [ABSTRACT FROM AUTHOR]