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Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications

In: Differential and Integral Inequalities

Author

Listed:
  • Artion Kashuri

    (University Ismail Qemali of Vlora)

  • Rozana Liko

    (University Ismail Qemali of Vlora)

Abstract

The authors discover a general integral identity concerning (n + 1)-differentiable mappings defined on m-invex set via Caputo k-fractional derivatives. By using the notion of generalized ((h 1, h 2);(η 1, η 2))-convex mappings and this integral equation as an auxiliary result, we derive some new estimates with respect to Hermite–Hadamard type inequalities via Caputo k-fractional derivatives. It is pointed out that some new special cases can be deduced from main results. At the end, some applications to special means for different positive real numbers are provided as well.

Suggested Citation

  • Artion Kashuri & Rozana Liko, 2019. "Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications," Springer Optimization and Its Applications, in: Dorin Andrica & Themistocles M. Rassias (ed.), Differential and Integral Inequalities, pages 435-458, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-27407-8_14
    DOI: 10.1007/978-3-030-27407-8_14
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