Some results on integral inequalities via Riemann–Liouville fractional integrals

• Main Authors: Xiaoling Li, Shahid Qaisar, Jamshed Nasir, Saad Ihsan Butt, Farooq Ahmad, Mehwish Bari, Shan E Farooq
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: Journal of Inequalities and Applications
• Subjects: Simpson’s inequality; Convex functions; Power-mean inequality; Riemann–Liouville fractional integral
• Online Access: http://link.springer.com/article/10.1186/s13660-019-2160-1
• ISSN: 1029-242X

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.