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 (Formula presented.) -convex stochastic processes (Formula presented.) using center and radius (Formula presented.) order with the notion of interval valued functions (Formula presented.). By utilizing this definition and Mean-Square Fractional Integrals, we generalize fractional Hermite–Hadamard–Mercer-type inclusions for generalized (Formula presented.) 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 (Formula presented.). Also, our work uses interesting examples of (Formula presented.) with Python-programmed graphs to validate our findings using an extension of Mercer’s inclusions with applications related to entropy and information theory.