This talk addresses the numerical solution of fractional differential equations with various boundary conditions. We introduce a unified spectral penalty method (SPM) framework, employing different basis functions for Riemann-Liouville and Caputo formulations. Our analysis establishes the method's stability and provides a principled way to choose penalty parameters. The presented numerical results, including comparisons with existing methods, validate the theory and showcase the superior performance and high accuracy of the proposed SPM.