Abstract
In this paper, a new study is dealt and presented the nonlinear control system consists of nonlinear differential equations of fractional orders with a mixture of ordinary derivatives of the first and second order that are unstable before feedback gain, we will study this nonlinear control system after feedback gain and prove the local asymptotically stable of the system by using a set of conditions that illustrated the stability of these systems, the work was reinforced with application examples that were programmed to reach illustrations that show the stability of the systems offered with high efficiency and accuracy.
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