Some results on integral inequalities via Riemann–Liouville fractional integrals

Journal of Inequalities and Applications

Shahid Qaisar¹  Jamshed Nasir¹  Saad Ihsan Butt¹  Shan E Farooq²  Mehwish Bari³  Xiaoling Li⁴  Farooq Ahmad⁵ 

[1] Department of Mathematics, COMSATS University Islamabad;Department of Mathematics, GC University;Department of Mathematics, NCBA&E;School of Information Science and Engineering, Chengdu University;School of Mechanical and Aerospace Engineering, NANYANG Technological University;

关键词: Simpson’s inequality;    Convex functions;    Power-mean inequality;    Riemann–Liouville fractional integral;   

DOI  :  10.1186/s13660-019-2160-1

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown