The rapid expansion of multimedia data in fields like healthcare and finance necessitates robust image encryption to protect sensitive content. Conventional chaotic encryption, based on integer-order systems, is hindered by restricted key spaces (e.g., \(\varvec{2}^{\varvec{100}}\) and suboptimal parameter choices, exposing vulnerabilities. This work introduces an innovative encryption method that merges a fractional-order chaotic Logistic map with neural network optimization to overcome these shortcomings and enhance security. Utilizing the Grunwald-Letnikov derivative, the fractional-order Logistic map produces a complex, unpredictable sequence for encryption. A feedforward neural network fine-tunes parameters ( \(\varvec{r = 3.9945} \) , \(\varvec{x_0 = 0.1035} \) ), elevating the Lyapunov exponent from 0.5032 to 0.6540, signifying heightened chaos. This integration harnesses fractional-order memory effects and neural network adaptability, surpassing traditional integer-order encryption constraints. The method achieves a key space of \(\varvec{2}^{\varvec{256}}\) , entropy of 7.9962, and horizontal correlation of 0.0028. Parameter sensitivity tests show significant output variation with minor changes. Security analysis yields NPCR at 99.60% and UACI at 33.45%. Neural network training achieves a low mean squared error of 0.0032912 by epoch 100, with high correlation \(\varvec{R > 0.99} \) . Encryption of 256 \(\times \) 256 images in 0.21 seconds and 720p video at 41.67 fps (0.024 s/frame) supports real-time applications. By combining fractional-order chaos with machine learning, this approach delivers superior image encryption, addressing integer-order system limitations. It provides a scalable framework for secure multimedia communications. Future efforts will extend the technique to color images and video, incorporating advanced machine learning for greater resilience.
