Solving Hilfer fractional dirac systems: a spectral approach

Abstract

In this study, we define Hilfer fractional Dirac system. Our main object is to analyze the main spectral structure of the Hilfer fractional Dirac system. To this end, the self-adjointness of the Hilfer fractional Dirac operator, orthogonality of the eigen-vector-functions, and reality of the eigenvalues are displayed. Also, we obtain the representation of the solution of the system by using Laplace transforms with analytical estimations. We investigate eigen-vector functions and eigenvalues for the Hilfer fractional Dirac boundary value problem and illustrate the results in detail with tables and figures.