Conformable fractional Dirac system on time scales

Abstract

We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale T. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on T. So, we provide a constructive procedure for the solution of this problem. These results are important steps to consolidate the link between fractional calculus and time scale calculus in spectral theory.