To address traditional image encryption’s drawbacks of high computational complexity, insufficient key space, and weak anti-attack capability, this study proposes a novel encryption system integrating fractional-order chaos and dual biological encoding, i.e. a four-dimensional fractional-order discrete-time hopfield neural network (F-DHNN) embedded with locally active memristors, which is constructed using the Caputo fractional difference operator to enhance nonlinear complexity and long-memory characteristics. The systematic dynamic analyses via Lyapunov exponent spectra, bifurcation diagrams, and phase portraits focused on key parameters w₂₂, q, and k₁ reveal pronounced hyperchaotic behavior at w₂₂ = 2.2, q = 0.6, and k₁ = 2.75 (with multiple positive Lyapunov exponents), whereas the locally active memristor, validated by hysteresis loops and DC V-I characteristics, contributes nonvolatility and local activity to the network’s rich dynamics. The encryption mechanism integrates RNA dynamic transcription (three rounds of pairing, mutation, insertion/deletion) and DNA encoding (8 dynamic rules, base XOR), combined with 16 rounds of triple hybrid diffusion and global cyclic shifting. The security tests show that the encrypted images have information entropy of 7.9991 (near the theoretical maximum 8), NPCR of 99.6033%, and UACI of 33.4540%, which are close to their corresponding ideal values, with adjacent pixel correlation approaching zero, enabling resistance to 25% cropping and 10% salt-and-pepper noise attacks; hardware implementation on an ARM (STM32) platform confirms consistency with simulations, and this system that features linear time complexity (O(M×N )), outperforms single-mechanism schemes, providing high security and engineering feasibility for sensitive image transmission.