In this paper we concern with asymptotic stability, synchronization control and numerical solution of incommensurate order fractional Shimizu-Morioka dynamical system. Firstly we prove the existence and uniqueness of the solutions via a new theorem. After finding steady-state points, we obtain necessary and sufficient conditions for the asymptotic stability of the Shimizu-Morioka system. We also study the synchronization control where we employ master-slave synchronization scheme. Finally, employing Adams-Bashforth-Moulton's technique we solve the Shimizu-Morioka system numerically. To the best of our knowledge, there exist not any study about analysis of chaotic dynamics of fractional Shimizu-Morioka system in the literature. In this sense the present paper is going to be a totally new contribution and highly useful research for synthesis of a nonlinear system of fractional equations.