Bullen-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings with Applications

Abstract

In this paper, we first introduce a novel extension of the Bullen-type inequalities using Riemann-Liouville integral operators and establish a generalized fractional integral identity of the Bullen type. Next, we derive integral inequalities related to the Bullen-type inequalities for twice-differentiable mappings, utilizing this novel extended identity. To demonstrate these inequalities, we provide examples along with corresponding graphs. Furthermore, we investigate how these inequalities can be practically applied to mean inequalities, contributing to a deeper comprehension and wider usefulness of these mathematical ideas. Finally, the inequalities given in this work extend several known inequalities in the literature, which is the main advantage of the newly found inequalities.