Investigation of solutions of Abel's integral eqyations

In this study, Abel integral equations, generalised Abel integral equations and second kind weak Volterra integral equations are considered. In addition, the Laplace transform method, Adomian decomposition, method of successive approximations and Homotopy analysis transform method are used to solve these equations. This thesis consists of five chapters. In the first chapter, a brief summary of the literature on Abel integral equations is given. In the second chapter, the basic definitions we will use are mentioned. In the third chapter, the methods we will use to solve these equations are introduced. In the fourth section, weakly singular Volterra integral equations are solved by Laplace transform, Adomian decomposition, successive approximations and the Homotopy analysis transform method. In addition, Abel integral equations are solved by Homotopy analysis transformation and Laplace transform method. Finally, in the fifth chapter, suggestions for future work on these problems are given.