On the Center-Radius Order (P,m)-Superquadratic Interval Valued Functions and Their Fractional Perspective with Applications

In this paper, we introduce, for the first time, a novel class of (center-radius order (P,m)-superquadratic interval-valued functions) cr-(P,m)-superquadratic IVFs, and systematically investigate their fundamental structural properties. Building upon these properties, we establish new Jensen and Hermite–Hadamard (HH) type inequalities, together with their fractional extensions formulated via Riemann–Liouville (RL) fractional integral operators within the setting of interval calculus. The validity and sharpness of the derived results are illustrated through numerical examples and graphical representations. Moreover, the theoretical developments are further enriched by applications in information theory, leading to meaningful generalizations and notable improvements over several existing results reported in the literature.