Generalized Fractal–Fractional Integral Inequalities on Fractal Sets with Applications

Abstract

In this study, we establish a set of novel Bullen-type inequalities applicable to differentiable convex functions within the framework of extended fractional integrals in a fractal domain. The key benefit of employing these inequalities and associated operators lies in their versatility, allowing the conversion of these inequalities into established results for Riemann integrals. Additionally, they give rise to new inequalities applicable to Riemann-Liouville fractional integral inequalities, as well as generalized Riemann-Liouville fractional integral inequalities. To bolster the relevance of the conclusions, we also present the applications of recently developed results regarding the probability density functions, the quadrature formulae and the special means.