<p>Mittag-Leffler stabilization (MLS) of nonlinear dynamical systems via Caputo’s fractional order derivative (NSCFD) by boundary and distributed controls is our challenge in this work. In fact, both distributed and Dirichlet boundary controllers have been designed for the MLS of the NSCFD. Using some inequality techniques and a Lyapunov’s method, some sufficient conditions have been established to obtain the MLS of NSCFD by distributed and Dirichlet boundary controls. Also, we have proved that the unbounded operator associated to the NSCFD is the infinitesimal generator of a strongly continuous semi-group of contractions on a Hilbert space. Consequently, the existence and uniqueness of a global solution to the NSCFD have been proved for NSCFD with homogeneous and non-homogeneous Dirichlet boundary conditions and source terms. Finally, we have presented some numerical experiments to justify and show the effectiveness and the robustness of the designed distributed and Dirichlet boundary controllers.</p>