Korean J. Math. Vol. 27 No. 2 (2019) pp.357-374
DOI: https://doi.org/10.11568/kjm.2019.27.2.357

$k-$fractional integral inequalities for $(h-m)-$convex functions via Caputo $k-$fractional derivatives

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Published: Jun 30, 2019
Keywords:
Caputo fractional derivatives, Caputo $k-$fractional derivatives, $(h-m)-$convex functions
Mathematics Subject Classification:
26B15, 26A51, 34L15.

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Lakshmi Narayan Mishra
Department of Mathematics, School of Advanced Sciences Vellore Institute of Technology (VIT) University Vellore 632 014, Tamil Nadu, India
Qurat Ul Ain
COMSATS University Islamabad, Attock Campus, Pakistan.
Ghulam Farid
COMSATS University Islamabad, Attock Campus, Pakistan.
Atiq Ur Rehman
COMSATS University Islamabad, Attock Campus, Pakistan.

Abstract

In this paper, first we obtain some inequalities of Hadamard type for $(h-m)-$convex functions via Caputo $k-$fractional derivatives. Secondly, two integral identities including the $(n+1)$ and $(n+2)$ order derivatives of a given function via Caputo $k-$fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo $k-$fractional derivatives have been proved.


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References

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