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This study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for differentiable convex functions. In the findings section, firstly, an integral identity is obtained and various integral inequalities are obtained based on this identity. The peculiarity of the results is that a hybrid operator has been used in inequality theory, which includes the derivative and integral operators together. [ABSTRACT FROM AUTHOR]

In this article, firstly, Hermite–Hadamard's inequality is generalized via a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. Then a new kernel is obtained and a new theorem valid for convex functions is proved for fractional order integrals. Also, some applications of our main findings are given. [ABSTRACT FROM AUTHOR]

In this paper, we present the notion of (g, φh,m) -convex and (g, log φ) -convex dominated function and present some properties of them. Besides, we attain some Hermite-Hadamard-type inequalities for (g, φh,m) -convex and (g, log φ) -convex dominated functions. Our results generalize some findings about Hermite-Hadamard-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

We gathered several new integral inequalities with the help of a kernel and using functions which are convex. The proofs are made with quite basic analysis and stated on Hölder and Power mean inequalities. [ABSTRACT FROM AUTHOR]

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