Some solution methods of linear bigeometric volterra integral equations

The aim of this study is to provide new alternative solution methods for linear bigeometric Volterra integral equations. In the first part of this study, which consists of six chapters, a literature review is made and information about the historical development, importance and application areas of the subject is given. In the second chapter, the basic definitions, theorems and propositions needed for the thesis are stated. In the third chapter, by utilizing the definition of bigeometric integral equation in the literature, the classifications of integral equations are transferred to bigeometric calculus in its most general form and the relationship between bigeometric integral equations and bigeometric differential equations is examined and expressed with examples. The main findings of the thesis are presented in the fourth and fifth chapters. In the fourth chapter, the homotopy perturbation method is transferred to bigeometric calculus and the application of the bigeometric homotopy perturbation method to bigeometric differential equations and linear bigeometric Volterra integral equations is given. In the fifth chapter, the differential transformation of a function in bigeometric calculus is defined and the basic theorems needed to apply the bigeometric differential transformation method are proved. With the help of the properties obtained, the solutions of bigeometric differential equations and linear bigeometric Volterra integral equations are analyzed with examples. In the last chapter, the results and evaluations obtained in the thesis are given.