This paper investigates a class of uncertain fractional-order delayed cellular neural networks (UFODCNNs) with fuzzy operators and nonlinear activations. Both fuzzy AND and fuzzy OR are considered, which help to improve the robustness of the model when dealing with various uncertain problems. To achieve the finite-time (FT) synchronization and Mittag–Leffler synchronization of the concerned neural networks (NNs), a nonlinear adaptive controller consisting of three information feedback modules is devised, and each submodule performs its function based on current or delayed historical information. Based on the fractional-order comparison theorem, the Lyapunov function, and the adaptive control scheme, new FT synchronization and Mittag–Leffler synchronization criteria for the UFODCNNs are derived. Unlike previous feedback controllers, the control strategy proposed in this article can adaptively adjust the strength of the information feedback, and partial parameters only need to satisfy inequality constraints within a local time interval, which shows our control mechanism has a significant advantage in conservatism. The experimental results show that our mean synchronization time and variance are $11.397\%$ and $12.5\%$ lower than the second-ranked controllers, respectively.

This paper investigates the fixed-time synchronization of fractional-order proportional delay Hopfield neural networks (PDHNNs) with bounded parameter uncertainties. Unlike constant delay and bounded variable delay, proportional delay has time-varying and unbounded characteristics, which pose challenges for the synchronization control of primary–secondary fractional neural networks. To achieve fixed-time synchronization, we propose a new nonlinear multi-module feedback controller. It consists of three key functional modules: eliminating the impact of proportional delay on system stability; ensuring convergence within a fixed time frame without being limited by initial conditions; and expanding the selectable range of parameters. Combining the stability lemma and inequality techniques, synchronization criteria of PDHNNs are derived based on the construction of a Lyapunov function with a negative fractional derivative. The settling time can be effectively estimated, which depends on the control parameters and is independent of initial values. Two numerical experiments verify the effectiveness of the theorem and corollary in this study.

Traditional human motion prediction methods attempt to discover the relationship between observed and future motion sequences. However, due to the dynamic complexity of human motion, existing methods cannot fully capture the interrelationships among motion sequences, and their performance remains unsatisfactory. In this work, we propose a novel Two-stage Refinement (TSR) framework for human motion prediction. It consists of two branches: (i) a traditional motion prediction branch for preliminary prediction, and (ii) an auxiliary refinement branch designed to estimate and compensate for the preliminary prediction errors. In this way, we can obtain better prediction performance than with traditional one-stage methods. To further bridge the gap between predicted results and groundtruth, we introduce a novel fractional-order differential loss function in this work. Existing methods use only integer-order differences to capture instantaneous state changes, often failing to account for the long-range temporal dependencies in human motion. By contrast, the inherent memory effect of the fractional-order differential loss function can account for long-term dependencies and enable precise tuning of high-order trajectory derivatives, thus yielding more physically realistic motion sequences with minimal error accumulation. Comparative experiments demonstrate that our proposed Fractional Optimization-based Two-stage Refinement Framework (FOTSR) outperforms most existing works on three benchmarks (including Human3.6M, CMU-Mocap, and 3DPW).