<p>Continuum robotics has received increasing attention, especially for its promising applications in complex unstructured environments. However, high-precision tracking control of continuum manipulators is a recognized challenge due to inaccuracies in kinematic modeling. The problem is addressed in this research using a novel tracking controller of unknown models based on fuzzy adaptive zeroing neural networks (FAZNN). In order to ensure the tracking accuracy and avoid the phenomenon of oscillation, the model-less tracking control will intelligently adjust the convergence factor according to the error. In the traditional zeroing neural networks (ZNN), a fuzzy adaptive control strategy is added. The proposed method can estimate the dynamic Jacobian matrix of continuum manipulators with unknown models by only the input–output information, and the feedback error can be used by the fuzzy control approach to adaptively change the convergence rate. Moreover, this paper employs five different activation functions including linear activation function (LAF), power-sigmoid activation function (PSAF), finite-time activation function (FATF), modified finite-time activation function (MFATF), and robust fixed-time activation function (RFTAF). The FATF and MFATF are investigated in the finite-time convergence feature, and RFTAF are investigated in the fixed-time convergence feature. In addition, the stability of the proposed control scheme is proved through the Lyapunov theory. Finally, the simulation results and comparisons are given to show that the proposed approach based on FAZNN can effectively improve tracking error accuracy and increase robustness in contrast with the using the conventional ZNN. The results demonstrate that MFATF and RFTAF outperforms other activation functions in terms of tracking robustness and accuracy.</p>