Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

Miguel Vivas-Cortez; Muhammad Uzair Awan; Sadia Talib; Guoju Ye; Muhammad Aslam Noor; Miguel Vivas-Cortez; Muhammad Uzair Awan; Sadia Talib; Guoju Ye; Muhammad Aslam Noor

doi:10.3934/math.2022567

AIMS Mathematics

2022, Volume 7, Issue 6: 10195-10214. doi: 10.3934/math.2022567

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Research article

Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

1.
Escuela de Ciencias Fisicas y Matematicas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Catolica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
College of Science, Hohai University, Nanjing 210098, Jiangsu, China
4.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 21 August 2021 Revised: 02 February 2022 Accepted: 22 February 2022 Published: 22 March 2022
MSC : 26A51, 26D15, 26A33

The main objective of this paper is to derive some new variants of trapezium like inequalities involving $ k $-fractional integrals with exponential kernel essentially using the definition of preinvex functions. Fractional bounds associated with some new fractional integral identities are also obtained. In order to show the significance of our main results, we also discuss applications to means and $ q $-digamma functions. We discuss special cases which show that our results are quite unifying.
- convex,
- preinvex,
- fractional,
- exponential,
- trapezium inequalities
Citation: Miguel Vivas-Cortez, Muhammad Uzair Awan, Sadia Talib, Guoju Ye, Muhammad Aslam Noor. Fractional identities involving exponential kernel and associated fractional trapezium like inequalities[J]. AIMS Mathematics, 2022, 7(6): 10195-10214. doi: 10.3934/math.2022567

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Abstract

The main objective of this paper is to derive some new variants of trapezium like inequalities involving $ k $-fractional integrals with exponential kernel essentially using the definition of preinvex functions. Fractional bounds associated with some new fractional integral identities are also obtained. In order to show the significance of our main results, we also discuss applications to means and $ q $-digamma functions. We discuss special cases which show that our results are quite unifying.

References

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