In this manuscript, we offer a systematic calculative algorithm to solve the one{dimensional fractional Dirac operator. The method of solution is according to utilizing the series solution to convert the governing system of fractional differential equations into a linear system of algebraic equations. We obtain the corresponding polynomial characteristic equations for some types of boundary conditions relying on the polynomial expansion and integral technique. Therewith, the eigenvalues can be discovered simultaneously from the multi{roots. Finally, we use some numerical examples to show that this method includes to demonstrating the validity and applicability of the technique.
