<p>This paper delves into the state estimation and finite-time (FT) synchronization for fractional neural networks with time delayed. Firstly, a Luenberger observer is proposed to estimate the unknown state. Secondly, the controller with sign or saturation functions is designed to achieve FT synchronization, which the saturation functions is utilized to avoid chattering phenomenon. Correspondingly, several algebraic-form-based synchronization criteria and the setting times are presented by means of the Jensen inequality, fractional-order Razumikhin theorem and fractional-order calculus property. Finally, two examples are listed to illustrate the correctness of the adopted approaches.</p>