Hermite–Hadamard type inequalities for conformable fractional integrals

Abstract

In this paper, first, we prove an identity for conformable fractional integrals. Second, by using this identity we will present some integral inequalities connected with the left hand side of the Hermite–Hadamard type inequalities for conformable fractional integrals. At the end, applications to some special means and error estimates for the midpoint formula are provided.

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Acknowledgements

The authors express their sincere thanks to the referees for careful reading of the manuscript and very helpful suggestions that improved the current manuscript substantially.

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Correspondence to M. Adil Khan.

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Khan, M.A., Ali, T., Dragomir, S.S. et al. Hermite–Hadamard type inequalities for conformable fractional integrals. RACSAM 112, 1033–1048 (2018). https://doi.org/10.1007/s13398-017-0408-5

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Keywords

  • Convex function
  • Hermite–Hadamard inequality
  • Conformable derivative
  • Conformable integrals
  • Special means
  • Midpoint formula

Mathematics Subject Classification

  • 26D15
  • 26A51
  • 26A33
  • 26A42