Fractional Integral Inequalities of Riemann-Liouville Type for Higher-Order Differentiable Convex Mappings

Abstract

In this paper, we investigate several Riemann-Liouville fractional integral inequalities for higher-order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right-hand side of the fundamental Hermite-Hadamard inequality to higher-order derivatives, along with its special cases. We also establish fractional inequalities for functions whose We also examined how fractional inequalities come out for functions whose higher-order derivatives, in absolute value, are convex. Lastly, we examine how to generalize the basic Hermite-Hadamard inequalities to fractional integral inequalities for functions whose derivatives of any order are convex. It is given which special case of this generalized integral yields the Hermite-Hadamard inequality.