Laplace integral transform and it's applications in bigeometric calculus

In this thesis, the Laplace integral transform in bigeometric analysis, which is one of the non-Newtonian analysis, is introduced by making use of the basic definitions and theorems of the Laplace integral transform, which is one of the integral transform methods of classical analysis. First of all, exponential arithmetic, which forms the basis of non-Newtonian analysis, is given. As in classical analysis, definitions of the concepts of limit, continuity, derivative and integral are given in bigeometric analysis. Afterwards, the definition of bigeometric Laplace integral transform in bigeometric analysis is made. Then, some basic concepts and theorems of the bigeometric Laplace integral transform are given. For this purpose, the definitions of bigeometric derivative, bigeometric indefinite integral and bigeometric definite integral in bigeometric analysis and the properties of these are used. In addition, the properties of the bigeometric Laplace integral transform are examined and the solutions of some bigeometric linear differential equations are investigated with the help of the bigeometric Laplace integral transform. These studies are supported by examples.