  The purpose of this article is to introduce the original results which
devoted with the nonlinear control system problems involves of nonlinear
differential equations of fractional orders. Thus, this system is described
with a mixed of ordinary derivatives in the first and second order that, are
unstable before feedback gain. More precisely, we investigate and analysis the
nonlinear control system in related to feedback gain matrix. In addition, we
prove that the considered system is locally asymptotically stabilizable via
certain conditions. Then, this work reinforce through some application examples
that programmed for illustrating and showing the stabilizability of the current
systems with high efficiency and accuracy.
