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Hermite-Hadamard inequality for new generalized conformable fractional operators

Authors :
Muhammad Adil Khan
Tahir Ullah Khan
Source :
AIMS Mathematics, Vol 6, Iss 1, Pp 23-38 (2021)
Publication Year :
2021
Publisher :
AIMS Press, 2021.

Abstract

This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a novel identity containing the new GC fractional integral operators is proved. By using this identity, a bound for the absolute of the difference between the two rightmost terms in the newly-established Hermite-Hadamard inequality is obtained. Also, some relations of our results with the already existing results are presented. Conclusion and future works are presented in the last section.

Details

Language :
English
ISSN :
24736988
Volume :
6
Issue :
1
Database :
OpenAIRE
Journal :
AIMS Mathematics
Accession number :
edsair.doi.dedup.....cf67d2636667130ac2486d2c4b06ed9a
Full Text :
https://doi.org/10.3934/math.2021002/fulltext.html