Some generalized Hadamard–type inequalities via fractional integrals

The study presents some generalized inequalities of the Hermite–Hadamard type using fractional Riemann–Liouville integrals for the class of $s$-convex functions in the first and second sense. The results are obtained for functions whose second derivatives are convex and take values at intermediate points of the interval. It is shown that with this approach, the absolute error of Hadamard–type inequalities decreases by a multiple of the number of intermediate points. In a particular case, the obtained upper bounds for the Hadamard inequality coincide with those in the literature.