In this paper, the variable order fractional permanent magnet synchronous motor (VOFPMSM) is investigated.
Conditions for existence and uniqueness of the solution of the VOFPMSM are proposed. The stability behavior of the system's
equilibrium points along with the variation of the motor parameters and the order of differentiation is discussed. Sufficient conditions
that guarantee the asymptotic stability of each of the equilibrium points of the system are established. Also, the required conditions that
give the effect of Hopf bifurcation of the system are established in terms of the system parameters and the order of differentiation and
consequently the appearance of the chaotic behavior of the VOFPMSM. New numerical techniques based on the modified backward
Euler's schemes for continuous and discontinuous variable order fractional model are presented. The obtained numerical results
demonstrate the merits of the proposed method and the variable order fractional permanent magnet synchronous motor over the
fractional permanent magnet synchronous motor.