Degenerate laplace transform and degenerate gamma function

Objective: This study aims to give the definition and properties of degenerate exponential, degenerate Euler, and degenerate Gamma functions, and the definition and some applications of the degenerate Laplace transform. Material and Methods: All articles and books written on the subject are the materials of the study. As a research technique, the articles given in the references section were examined and then the study was carried out using mathematical proof methods. Results: The thesis consists of five chapters. After the introduction, the second chapter summarises the references used in the thesis. The third chapter introduces the gamma function, the beta function and the Laplace transform and gives some theorems that will be used in the rest of the thesis. In the fourth chapter the degenerate exponential, degenerate Euler and degenerate Gamma functions are given with their properties. The degenerate Laplace transform is also introduced and some applications and relations to the Laplace transform are given. Conclusion: In this thesis, degenerate Gamma and degenerate Laplace transforms, which are related to the Gamma function and the Laplace transform, are introduced, their properties are studied in detail and the results obtained in this subject are given with their proofs.