Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville <em>k</em>-fractional integrals

Abstract

Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville k-Fractional integrals via convex functions. We established some new Ψ-Riemann-Liouville k-Fractional integral inequalities. We also give Ψ-Riemann-Liouville k-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.

Keywords

• convex function
• hermite-hadamard inequality
• jensen inequality
• jensen-mercer inequality
• hölder inequality
• improved power mean integral inequality
• <i>ψ</i>-riemann-liouville <i>k</i>-fractional integrals