Generalized integral inequalities for ABK-fractional integral operators

Saad Ihsan Butt; Erhan Set; Saba Yousaf; Thabet Abdeljawad; Wasfi Shatanawi; Saad Ihsan Butt; Erhan Set; Saba Yousaf; Thabet Abdeljawad; Wasfi Shatanawi

doi:10.3934/math.2021589

AIMS Mathematics

2021, Volume 6, Issue 9: 10164-10191. doi: 10.3934/math.2021589

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Research article

Generalized integral inequalities for ABK-fractional integral operators

1.
Department of Mathematics, COMSATS University, Islamabad, Lahore Campus, Pakistan
2.
Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey
3.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
6.
Department of Mathematics, Hashemite University, Zarqa, Jordan

Received: 05 March 2021 Accepted: 29 June 2021 Published: 09 July 2021
MSC : 26A33, 26A51, 26D10

In this paper, we employ new version of the Atangana-Baleanu integral operator namely $ ABK $-fractional integrals to obtain two general integral identities complying second-order derivatives for a given function. Thus allowing us to derive new generalized Hermite-Hadamard type inequalities via $ ABK $- fractional integrals. Moreover we give several new versions of Mid-point and Trapezoid type inequalities by employing Hölder, Young and Jensen inequalities.
- differentiable convex functions,
- Hölder inequality,
- Young inequality,
- power mean inequality,
- Katugampola fractional integral,
- AB-fractional integral,
- ABK-fractional integral
Citation: Saad Ihsan Butt, Erhan Set, Saba Yousaf, Thabet Abdeljawad, Wasfi Shatanawi. Generalized integral inequalities for ABK-fractional integral operators[J]. AIMS Mathematics, 2021, 6(9): 10164-10191. doi: 10.3934/math.2021589

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Abstract

In this paper, we employ new version of the Atangana-Baleanu integral operator namely $ ABK $-fractional integrals to obtain two general integral identities complying second-order derivatives for a given function. Thus allowing us to derive new generalized Hermite-Hadamard type inequalities via $ ABK $- fractional integrals. Moreover we give several new versions of Mid-point and Trapezoid type inequalities by employing Hölder, Young and Jensen inequalities.

References

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