In this paper, we prove some new generalizations of dynamic Opial-type inequalities on time scales. From these inequalities, as special cases, we formulate some integral and discrete inequalities proved in the literature and also extend some obtained dynamic inequalities on time scales. The main results are proved by using some algebraic inequalities, Hölder's inequality, and a simple consequence of Keller's chain rule on time scales.

In this paper, we will state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in the literature but also improve some of them. The main results will be proved by using some algebraic inequalities, the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. As special cases of the obtained dynamic inequalities, we will get some continuous and discrete inequalities.