Inequalities with parameters for twice-differentiable functions involving Riemann--Liouville fractional integrals

Abstract

In this paper, it is given an equality for twice-differentiablefunctions whose second derivatives in absolute value are convex. By usingthis equality, it is established several left and right Hermite--Hadamardtype inequalities and Simpson type inequalities for the case of Riemann--Liouville fractional integral.Namely, midpoint, trapezoid and also Simpson type inequalities are obtained forRiemann--Liouville fractional integral by using special cases of mainresults.