In this paper, the fractional Dirac operator with Caputo’s fractional derivative is considered. By using Laplace transform, the fractional Dirac operator reduces to an algebraic equation. Then by applying the inverse Laplace transform, we obtain the closed form of the characteristic function according to the two–parameters Mittag–Leffler function. By truncating the series of Mittag–Leffler function, the eigenvalues and the corresponding eigenfunctions are approximated. A convergence analysis for the proposed procedure is given. Finally, the efficiency and simplicity of the method are shown with some examples.
