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In this paper, we prove some new dynamic inequalities similar to Hardy's inequality on time scales T. The results as special cases when T = R contain continuous inequalities similar to Hardy's inequality, and when T = Z, the results contain discrete inequalities that are essentially new to the best of the authors' knowledge. R and Z denote the set of all real numbers and the set of all integers, respectively. Our main results are proved by using the Holder € inequality, Chain rule, and some properties of multiple integrals on time scales. Furthermore, some applications and examples are given to illustrate the investigated results. [ABSTRACT FROM AUTHOR]