FRACTIONAL INTEGRAL INEQUALITIES FOR SUPERQUADRATIC FUNCTIONS VIA ATANGANA–BALEANU’S OPERATOR WITH APPLICATIONS

In this paper, the notion of superquadraticity is used to obtain some new Fejér and Hermite–Hadamard-type inequalities by means of Atangana–Baleanu’s fractional integral operators. We determine improved versions of existing results for those superquadratic functions which are also convex. Findings from the study are verified by certain reduced results, numerical calculations and graphical depictions that takes few appropriate examples into account. The fact that the work has been improved using applications of type-1 modified Bessel functions, special means and moment of random variables by describing certain novel functions in the context of modified Bessel functions and taking uniform probability density function into consideration is another motivating aspect of the research. The research presented in this publication is new concerning the concept of superquadraticity. We are quite optimistic that this has the potential to make substantial input to encouraging further research.