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Research Article | Open Access

Fractional identities involving exponential kernel and associated fractional trapezium like inequalities

Miguel Vivas-Cortez1, Muhammad Uzair Awan2( ), Sadia Talib2, Guoju Ye3, Muhammad Aslam Noor4
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
Department of Mathematics, Government College University, Faisalabad, Pakistan
College of Science, Hohai University, Nanjing 210098, Jiangsu, China
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
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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.

Keywords

convexpreinvexfractionalexponentialtrapezium inequalities
CLC number: 26A51, 26D15, 26A33

References

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10195-10214
DOI: 10.3934/math.2022567

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Cite this article:
Vivas-Cortez M, Awan MU, Talib S, et al. Fractional identities involving exponential kernel and associated fractional trapezium like inequalities. AIMS Mathematics, 2022, 7(6): 10195-10214. https://doi.org/10.3934/math.2022567

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Received: 21 August 2021
Revised: 02 February 2022
Accepted: 22 February 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)