Applications of Laplace transform on time scales

The Laplace transform is very important for the solution of linear differential equations and systems of equations. A transformation that is so important in the classical sense is generalized to the time scale in this study. Later, Dirac dynamic equation system, which is also very important in quantum physics, was solved by Laplace transform on time scale. After defining Laplace transform and inverse Laplace transform in the first part of the study, its rules are given in detail and its application to the systems is explained in detail. Then, the concept of time scale is explained and important concepts such as derivative, integral and generalized integral are given in the time scale. Finally, Laplace transform is given on the time scale, how it is applied to dynamic systems and initial value problems including the Dirac dynamic equation system are solved on the time scale using this transformation. The concept of convolution, which is an important concept in the Laplace transformation, has been explained both in the classical case and on the time scale. For some cases, different versions of Dirac's dynamic equation system are solved using Laplace transform.