Some results on integral inequalities via Riemann–Liouville fractional integrals

Abstract

Abstract In current continuation, we have incorporated the notion of s−(α,m) $s- ( {\alpha,m} ) $-convex functions and have established new integral inequalities. In order to generalize Hermite–Hadamard-type inequalities, some new integral inequalities of Hermite–Hadamard and Simpson type using s−(α,m) $s- ( {\alpha,m} ) $-convex function via Riemann–Liouville fractional integrals are obtained that reproduce the results presented by (Appl. Math. Lett. 11(5):91–95, 1998; Comput. Math. Appl. 47(2–3): 207–216, 2004; J. Inequal. Appl. 2013:158, 2013). Applications to special means are also provided.

Keywords

• Simpson’s inequality
• Convex functions
• Power-mean inequality
• Riemann–Liouville fractional integral