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

Saad Ihsan Butt; Artion Kashuri; Muhammad Umar; Adnan Aslam; Wei Gao; Saad Ihsan Butt; Artion Kashuri; Muhammad Umar; Adnan Aslam; Wei Gao

doi:10.3934/math.2020334

AIMS Mathematics

2020, Volume 5, Issue 5: 5193-5220. doi: 10.3934/math.2020334

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Research article

Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals

1.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan
2.
Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, Vlora, Albania
3.
Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore(RCET) 54000, Pakistan
4.
School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China

Received: 25 April 2020 Accepted: 11 June 2020 Published: 15 June 2020
MSC : 26A33, 26A51, 26D07, 26D10, 26D15

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.
Citation: Saad Ihsan Butt, Artion Kashuri, Muhammad Umar, Adnan Aslam, Wei Gao. Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals[J]. AIMS Mathematics, 2020, 5(5): 5193-5220. doi: 10.3934/math.2020334

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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.

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