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

Artion Kashuri () and Rozana Liko ()
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Artion Kashuri: University Ismail Qemali of Vlora
Rozana Liko: University Ismail Qemali of Vlora

A chapter in Differential and Integral Inequalities, 2019, pp 435-458 from Springer

Abstract: 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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-27407-8_14

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DOI: 10.1007/978-3-030-27407-8_14

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