There are many well-known analogies in the concepts of difference calculus and differential calculus. The theory of measure chains was first introduced by Stefan
Hilger in his PhD thesis [27] in 1988 in order to unify continuous and discrete analysis. The general idea is to prove a result for a dynamic equation where the domain
of the unknown function is a so-called time scale, which may be an arbitrary closed subset of the reals. In view of the calculus and linear theory initiated by Aulbach
and Hilger [10, 11, 12, 28], in this thesis with the aim of providing a unified general framework, we have obtained in the time scale set-up some basic Opial Type
inequalities which have many important applications both in the continuous and discrete cases in many areas of applicable analysis. Finally, having the above
developed tools at our disposal, we give some results concerning upper bound estimates and uniqueness for the solutions of I.V.P.'s on time scale, which unify and
generalize many previously obtained results

Keywords : Opial Inequalities, Time Scales, Upper Bounds and Uniqueness of Solutions of I.V.P.'s