2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167682The theory and applications of dynamic derivatives on time scales has recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-$α$ derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen's inequality on time scales via the diamond-$α$ integral and present some corollaries, including Hölder's and Minkowski's diamond-$α$ integral inequalities.This is a preprint of an article whose final and definitive form will appear in the \emph{Journal of Inequalities and Applications}, http://www.hindawi.com/journals/jia/. Accepted 07/April/2008Classical Analysis and ODEs26D15; 39A13text