On fractional Bullen-type inequalities with applications

Integral inequalities in mathematical interpretations are a substantial and ongoing body of research. Because fractional calculus techniques are widely used in science, a lot of research has recently been done on them. A key concept in fractional calculus is the Caputo-Fabrizio fractional integral. In this work, we focus on using the Caputo-Fabrizio fractional integral operator to build a multi-parameter fractional integral identity. Using the obtained integral identity, certain generalized estimates of Bullen-type fractional inequalities have been generated. By establishing certain inequalities, this study advances the fields of fractional calculus and convex function research. Both graphical and numerical statistics are provided to show the correctness of our results. We finally provide applications to modified Bessel functions, $\mathfrak{h}$-divergence measures, and probability density functions.