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Hermite-Hadamard inequality for new generalized conformable fractional operators
- 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.
- Subjects :
- Pure mathematics
conformable integral
Inequality
hermite-hadamard inequality
General Mathematics
media_common.quotation_subject
lcsh:Mathematics
riemann-liouville operators
Conformable matrix
lcsh:QA1-939
Riemann hypothesis
symbols.namesake
Identity (mathematics)
Section (category theory)
generalized conformable fractional operators
Hadamard transform
Hermite–Hadamard inequality
symbols
Mathematics
media_common
Subjects
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