EXISTENCE RESULTS FOR A CONFORMABLE TYPE DIRAC SYSTEM ON TIME SCALES IN QUANTUM PHYSICS

Abstract

We consider a conformable (C-type) Dirac system under boundary conditions on a time scale, where this system is consistent with both principles of quantum mechanics and the theory of special relativity. Next, we generalize some principal spectral characteristics of usual Dirac systems to the C - type or case systems. Finally, some sufficient conditions are constructed to guarantee the existence of a solution for this problem on the given time scale by considering some fixed - point theorems. The last fixed - point theorem is proven in four cases.