One dimansionel conformable fractional order dirac equation

The Dirac equation is regarded as a revolutionary development in the history of modern physics. As a foundational equation of relativistic quantum mechanics, it not only successfully explains the half-spin (spin-½) nature of the electron but also predicts the existence of antiparticles, thereby opening a new era in theoretical physics. Furthermore, it provides an accurate description of the fine structure of the hydrogen atom spectrum. In this thesis, a one-dimensional conformable fractional-order Dirac equation, which can be considered as generalization of the classical Dirac equation, is studied. The work begins with an overview of the historical development of the subject, accompanied by the necessary preliminary background to facilitate a better understanding of the topic. Additionally, essential concepts and fundamental mathematical results used throughout the thesis are introduced. In the second and third chapters, the one-dimensional conformable fractional-order Dirac equation is examined in detail. The structure of the equation, its mathematical properties, and its physical interpretation are discussed comprehensively. Finally, the one-dimensional conformable fractional-order Dirac operator associated with the equation is analyzed in terms of its dissipative, accretive, and self-adjoint extensions, which are expressed through appropriate boundary conditions.