On the solution of a Sturm-Liouville problem by using Laplace transform on time scales

In this study, we solve a Sturm-Liouville problem on time scales with constant graininess by using Laplace transform which is one of the finest representatives of integral transformation used in applied mathematics. Eigenfunctions on the time scale were obtained in different cases with the Laplace transform. Thus, it was seen that the Laplace transform is an effective method on time scales. The results that will contribute to the spectral theory were obtained on the time scale with the examples discussed. It is very interesting that the results obtained differ as the time scale changes and this transformation can be applied to other types of problems. The problems that were established and solved enabled the subject to be understood on the time scale.