FPGA Implementation of Fractional-Order Hopfield Neural Network With Multi-Activation Functions

To enable accurate and resource-efficient hardware implementation of fractional-order neural networks for neuromorphic computing, an optimized hardware architecture for field programmable gate arrays (FPGA) is proposed, wherein Grünwald–Letnikov fractional calculus is integrated with Chebyshev optimal approximation techniques. First, a hardware-efficient FPGA-based Grünwald-Letnikov operator is developed by truncating the infinite memory term into a fixed window and quantizing binomial coefficients. Second, Chebyshev-optimized piecewise linear approximation is employed to implement nonlinear activation functions. The proposed approach achieves a 20-30% reduction in maximum error compared to traditional methods, implemented in a fractional-order heterogeneous memristive Hopfield neural network. The systematic integration of temporal optimization into functional modules achieves resource savings. In the experimental outcomes, excellent agreement with numerical simulations is observed. To demonstrate the practicality of the implemented fractional-order network, a pseudorandom number generator is designed, successfully passing all NIST SP 800-22 tests. This research advances computational efficiency in fractional-order neural networks, with substantial implications for their applications in secure communications and related domains.