The Riemann delta and Nabla integrals on time scales

The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis in 1988 in order to unify continuous and discrete analysis. For example, in this study differential equations and difference equations under the name of the dynamic equations is generalized.In this thesis, we consider Riemann Delta and Nabla integration on time scales. In chapter second, the basic definitions and theorems are given related to this subject.In third chapter, real-valued bounded functions defined on of Riemann delta integration is stated, smilarly the concepts of nabla integral are given briefly.In forth chapter, the concepts of Riemann integral on time scales are given. The Darboux definition of the integral is considered. Here we give also the Riemann definition of the integral on time scales and we prove the equivalence of the Darboux and Riemann definitions of the integral.Fundamental theorems of calculus on time scales are given in chapter fifth.Science Code: 39A10Key Words: Time Scale, Hilger derivative, Riemann delta integralPage Number: 51Adviser: Yrd. Doç. Dr. M. Seyyit SEYYİDOĞLU