On some qualitative behaviors of solutions of singular integral equations and integro-differential equations

This thesis consists of nine chapters; introduction, source-literature statement and material-method. In the fourth chapter, some basic results are given about the existence and uniqueness of solutions of integral equation (IEs) and integro-differential equations (IDEs). In the fifth chapter, classification of IEs is given. In the sixth part of this thesis, Volterra integro-differential equations (VIDEs), Volterra-Fredholm integro-differential equations (VFIDEs) , Laplace transformation method, some stability results about VIDEs and similar information are introduced. In Chapter 7, some qualitative behaviors of the solutions are examined with the help of Lyapunov's second method and fixed point method for certain singular and non-singular IEs which are available in the related literature. The eighth chapter examines some qualitative behaviors of the solutions of these kind equations with the help of known inequality techniques for a singular IDE with a small core, and the properties of the limitations of the solutions of a non-singular IDE. In the last chapter, some qualitative behaviors of the solutions of singular and non-singular integral equations which are available in the related literature are examined with the help of Lyapunov's second method and fixed point method. At the end of this thesis, a detailed literature about the thesis subject and the thesis subject is given. This thesis does not contain new and original result (s). In this thesis, it is aimed to present some information to the attention of the readers about the subjects in question.