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Hermite-Hadamard inequality for new generalized conformable fractional operators
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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.
American Institute of Mathematical Sciences (AIMS)
Title: Hermite-Hadamard inequality for new generalized conformable fractional operators
Description:
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.
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