  The 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-$\alpha$ 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-$\alpha$ integral and present some corollaries, including H\"{o}lder's
and Minkowski's diamond-$\alpha$ integral inequalities.
