Abstarct: Abstract In this thesis, the control problem of the adaptive cruise control system of cars, which are exposed to both modeling uncertainties and external disturbances, is considered by using the fractional order sliding mode control design. First, nonlinear dynamic and kinematic modeling of the adaptive cruise control model is presented, where the state variables are the distance between the front and rear cars. In the following, by applying modeling uncertainties and limited external disturbances, the model of this system has been rewritten in real conditions and in the presence of these disturbances. Next, in the first part, assuming a fixed and unknown upper band for the sum of uncertainties and disturbances, the sliding mode control law of the resistive-adaptive fractional order has been used to converge the rear car to the desired position in the desired cruise control arrangement. For this purpose, first, a stable fractional order sliding plane is defined. Then, using the Lyapunov theory, the fractional order sliding mode control law is designed to zero the sliding surface and prove the stability. In this method, it is not necessary to know the upper band of disturbances and uncertainties, and this upper band is estimated online through an adaptive rule. Finally, the finite time of convergence of the system to the sliding plane is obtained, a method to improve the discontinuity in the adaptive cruise controller is proposed, and a comparison between chattering in the fractional order mode and the corresponding positive order mode is made. In the second part, considering the nonlinear adaptive cruise control model, the limited time adaptive fractional order sliding mode control law is used to converge the system to the desired values of this load in a predetermined limited time. For this purpose, by considering the adaptive cruise model with modeling uncertainties in such a way that the dynamic parameters are unknown, a finite time fractional sliding plate has been designed, and its convergence is achieved in a certain finite time. In the following, the design of the fractional order sliding mode control law is discussed and the control law is designed along with the adaptive laws for the convergence of sliding planes to zero, and its stability is proved by using Lyapanov in finite time. In the last chapter, the simulation results show the correctness of the controllers designed in both parts to solve the problem of adaptive cruise control in the presence of disturbances with unknown upper bounds in the form of numerical examples.