Fractional Neural Field Modeling of Consciousness Transitions under Anesthesia: Multi-Scale Integration from Molecular Mechanisms to EEG Signatures

Consciousness arises from coordinated neural network activity but is exquisitely sensitive to molecular perturbations, such as those induced by anesthetic agents. Predicting how molecular-level pharmacology propagates through networks to produce EEG-level signatures remains a central challenge in neuroscience. Here, we introduce a fractional-order neural field model that rigorously integrates receptor dynamics (\(\:{GABA}_{A}\), NMDA, K2P channels), network connectivity, and fractional temporal derivatives to capture memory-dependent neural processes. The fractional order \(\:\alpha\:\:\in\:\:\left(\text{0,1}\right)\) quantitatively modulates transient growth, spectral EEG slopes, ERP amplitudes, and gray-zone dynamics near bifurcation thresholds. We establish well-posedness, spectral stability, and explicit bifurcation criteria, including fractional generalizations of classical pitchfork and Hopf transitions.Using synthetic experimental EEG datasets designed to replicate canonical empirical features (\(\:\frac{1}{{f}^{\beta\:}}\:\:\)scaling, alpha oscillations, ERP pulses), we validate the model through power spectral density comparisons, ERP waveform analyses, and stability domain mapping. Numerical simulations reproduce classical neural field phenomena while predicting novel testable behaviors: prolonged transients under ketamine, subexponential drifts in gray-zone anesthesia, and \(\:\alpha\:-\)dependent bifurcation shifts. By bridging molecular pharmacology, network dynamics, and EEG biomarkers in a reproducible simulation framework, this work provides a unifying, predictive model for consciousness transitions, with direct implications for anesthetic management and the mechanistic understanding of neural memory effects.