Fractional perspective of HH f-divergence, midpoint and trapezoidal type estimates for superquadratic function

Abstract

In this study, we take into account the notion of superquadraticity and come up with the fractional version of midpoint and trapezoidal types estimations for differentiable superquadratic function via Riemann–Liouville’s fractional integral operators. It is to be noted that the inequalities derived from superquadratic functions exhibit greater refinement in comparison to those derived from convex functions. The findings are validated through simplified results, numerical analyses, and graphical representations, using a selection of suitable examples. We also introduce the Hermite–Hadamard (HH) $f$-divergence for superquadratic function and obtain its associate properties via Riemann–Liouville’s fractional integral operators. The work is enhanced with applications of modified Bessel’s function of Type-1 and Mittag-Leffler function which is another motivating factor. The new results significantly extend and enhance the existing work available in the literature.