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

Lakshmi Narayan Mishra, Qurat Ul Ain, Ghulam Farid, Atiq Ur Rehman

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.

Keywords


Caputo fractional derivatives; Caputo $k-$fractional derivatives; $(h-m)-$convex functions

Subject classification

26B15, 26A51, 34L15.

Sponsor(s)



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References


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