Superquadraticity and its fractional perspective via center-radius cr-order relation

In this work, the total order relation between two intervals is used to define cr-superquadraticity. Some fundamental properties of cr-superquadratic functions are addressed. By employing such definitions and properties we show that under the cr-order relation, the definite integral of interval-valued functions is order-preserving. We develop inequalities of Jensen and Hermite–Hadamard types for cr-superquadratic interval-valued functions. We moreover utilise the concept of interval-valued superquadratic functions of Center-Radius cr-order to present fractional perspective of Hermite–Hadamard type inequalities and bring up with few particular cases. The findings are confirmed by graphical representations and numerical estimates based on certain appropriate examples. Another motivating component of the study is that it has been enriched with applications of special means, modified Bessel Function of first type and moment of random variables by defining some new functions in terms of modified Bessel Function and considering uniform probability density function. The findings in this paper are novel in the frame of cr-superquadratic interval-valued functions. We are quite optimistic that, this will make a substantial contribution to encouraging further research.