In this manuscript a new approach into analyzing the local stability of equilibrium points of non-linear Caputo fractional planar systems is shown. It is shown that the equilibrium points of such systems can be a stable focus or unstable focus. In addition, it is proposed that previous results regarding the stability of equilibrium points have been incorrect, the results here attempt to correct such results. Lastly, it is proposed that a Caputo fractional planar system cannot undergo a Hopf bifurcation, contrary to previous results prior. Though, it is shown that such systems can undergo a Hopf bifurcation (topologically).