In this manuscript, the pseudospectral method for solving the one--dimensional Caputo fractional Dirac operator are presented. The base of this method is transforming the problem to a weakly singular Volterra integro-differential equation. For this purpose first, the matrices obtained from the representation of the fractional integration operator based on Chebyshev cardinal functions. To obtain approximation of the eigenvalues of the problem, the roots of the characteristics matrix function are find. Finally, Some numerical examples are presented to illustrate the ability and accuracy of the method.
