Abstarct: The main purpose of this thesis is to analyze the stability of commensurate fractional order (FO) linear systems subject to saturation element. To this reason, first, a new stability condition is proposed to estimate the region of attraction using the Lyapunov direct method. Then, the stability of a certain class of FO non-linear systems under control saturation is investigated using the Granular-Bellman theorem and sector boundary condition. The stability analysis of the FO uncertain linear systems is also studied by means of the solution estimation of differential equation and the Lyapunov method. Finally, stability analysis of uncertain class of FO linear systems is discussed in the presence of state saturation. Simulation results illustrate the appropriate performance of the designed controllers.