A newly developed study into fractional Boole's inequalities through twice differentiable functions and application

Abstract

This study develops fractional Boole inequalities for $h$-convex functions utilizing Riemann-Liouville integral operators. This represents a novel variant of the established fractional Boole inequalities applicable to twice differentiable functions, derived through basic computations involving the $B$-function. Furthermore, new results regarding Boole inequalities related to $s$-convex functions and $P$-functions are introduced. Finally, an application for special means using different positive real numbers is given.