Some new generalizaitons of hadamard-type midpoint inequalities involving fractional integrals

Abstract

In this study, we formulate the identity and obtain some generalized inequalities of the Hermite-Hadamard type by using fractional Riemann-Liouville integrals for functions whose absolute values of the second derivatives are convex. The results are obtained by uniformly dividing a segment [a,b] into n equal sub-intervals. Using this approach, the absolute error of a Midpoint inequality is shown to decrease approximately n(2) times. A dependency between accuracy of the absolute error (epsilon) of the upper limit of the Hadamard inequality and the number (n) of lower intervals is obtained.