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In this paper, adaptive prescribed finite time stabilization of uncertain single-input and single-output nonlinear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a nonsingular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time estimations of the states and unknown parameters of the system. Moreover, particle swarm optimization algorithm is used to obtain the design parameters of the proposed disturbance observer and controller. To show the performance of designed control scheme, the proposed approach is employed to guarantee prescribed finite time stabilization of nonlinear vibration of a nonlocal strain gradient nanobeam. Finally, numerical simulations are performed to illustrate the effectiveness and performance of the developed adaptive control scheme for the vibration control of nanobeam in comparison to the conventional sliding mode control.