Tunc, TubaDemir, Izzettin2024-08-232024-08-2320241687-2770https://doi.org/10.1186/s13661-024-01852-4https://hdl.handle.net/20.500.12684/14057In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite-Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite-Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs.en10.1186/s13661-024-01852-4info:eu-repo/semantics/openAccessHermite-Hadamard-type inequalitiesMidpoint-type inequalitiesConvex functionsRiemann-Liouville fractional integralsProportional Caputo-hybrid operatorDifferentiable MappingsFractional DerivativesReal NumbersArticle202412-s2.0-85188778866WOS:001195391100004Q3N/A