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

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Differential and Integral Inequalities

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 151))

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Technical Science, University Ismail Qemali of Vlora, Vlorë, Albania

    Artion Kashuri & Rozana Liko

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  1. Artion Kashuri
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  2. Rozana Liko
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Editors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania

    Dorin Andrica

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Kashuri, A., Liko, R. (2019). Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications. In: Andrica, D., Rassias, T. (eds) Differential and Integral Inequalities. Springer Optimization and Its Applications, vol 151. Springer, Cham. https://doi.org/10.1007/978-3-030-27407-8_14

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