This paper proposes a strictly predefined-time convergent and anti-noise fractional-order zeroing neural network (SPTC-AN-FOZNN) model, meticulously designed for addressing time-variant quadratic programming (TVQP) problems. This model marks the first variable-gain ZNN to collectively manifest strictly predefined-time convergence and noise resilience, specifically tailored for kinematic motion control of robots. The SPTC-AN-FOZNN advances traditional ZNNs by incorporating a conformable fractional derivative in accordance with the Leibniz rule, a compliance not commonly achieved by other fractional derivative definitions. It also features a novel activation function designed to ensure favorable convergence independent of the model's order. When compared to five recently published recurrent neural networks (RNNs), the SPTC-AN-FOZNN, configured with $0<α\leq 1$, exhibits superior positional accuracy and robustness against additive noises for TVQP applications. Extensive empirical evaluations, including simulations with two types of robotic manipulators and experiments with a Flexiv Rizon robot, have validated the SPTC-AN-FOZNN's effectiveness in precise tracking and computational efficiency, establishing its utility for robust kinematic control.