| The dynamic equations on time scales, which have been created in order to unify the study of differential and difference equations,are a new area of mathematics that has recently received a lot of attention. Moreover, many results on this issue have been well documented in the monographs [1-14]. Especially, the study of stability, oscillation and initial-boundary value problems have achieved great progress. But, the investigative achievement of impulse problems, infinite delay problems and periodic problems on time scales are relatively fewer. It is just a new star, though a few of references are found (see [8, 15-16]), and many interesting problems in both theory and application are worth further researching.In this paper, we mainly study the existence of solutions of impulsive functional dynamic equations and functional differential inclusion on time scales. Our corresponding results are obtained via some new fixed point theorems. This paper is organized as follows. First chapter is the introduction, mainly introduce some results of former researchers with their methods, and present research at home and abroad, and the significance to study this paper. Simultaneously, we enumerate the problems of which will be solved in our paper.In the second chapter, we give some theoretical knowledge about time scales, which is the foundation of our subsequence works. The concepts and theoretical results in this chapter are coming from the investigation of Stefan Hilger and other mathematicians.In the third chapter, we will consider the existence of periodic solutions of impulsive integro-differential equations. In this chapter, by using a set contractive fixed point theorem, we will study the existence of periodic solutions of the following systems on the time scale:We will use a new fixed point theorem to obtain the sufficient condition of the existence of solutions of the differential inclusion and the maximum,minimum solution of the inclusion.
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