Integral inequalities of h-superquadratic functions and their fractional perspective with applications

Abstract

The purpose of this article is to provide a number of Hermite–Hadamard and Fejér type integral inequalities for a class of $h$-superquadratic functions. We then develop the fractional perspective of inequalities of Hermite–Hadamard and Fejér types by use of the Riemann–Liouville fractional integral operators and bring up with few particular cases. Numerical estimations based on specific relevant cases and graphical representations validate the results. Another motivating component of the study is that it is enriched with applications of modified Bessel function of first type, special means, and moment of random variables by defining some new functions in terms of modified Bessel function and considering uniform probability density function. The results in this paper have not been initiated before in the frame of $h$-superquadraticity. We are optimistic that this effort will greatly stimulate and encourage additional research.