Fractional Simpson Like Type Inequalities for Differentiable s-Convex Functions

Abstract

Convexity inequalities are very important for fractional calculus and its efficiency in many applied sciences. This field has become increasingly popular and represents a powerful tool for estimating errors of quadrature formulas. In this paper, we seek to develop new four-point Simpson-type inequalities involving Riemenn-Liouville integral operators. To do this, we first propose a new integral identity. By using this identity we establish some new fractional Simpson like type inequalities for functions whose first derivatives are s-convex in the second sense. 
Some particular cases are also discussed. We provid at the end some applications to special means to demonstrate the effectiveness of our results.

Key words and phrases. 3/8-Simpson inequality, Riemann-Liouville integral operators, s-convex functions, H¨older inequality.

2010 Mathematics Subject Classification. 26D10, 26D15, 26A51