Some parameterized Simpson-, midpoint- and trapezoid-type inequalities for generalized fractional integrals

Abstract

Abstract In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers.

Keywords

• Simpson’s 1 3 $\frac{1}{3}$ formula
• Integral inequalities
• Fractional calculus
• Convex functions