Precise, generalizable subject-agnostic seizure prediction (SASP) remains a fundamental challenge due to the intrinsic complexity and significant spectral variability of electrophysiological signals across individuals and recording modalities. We propose FAPEX, a novel architecture that introduces a learnable fractional neural frame operator (FrNFO) for adaptive time-frequency decomposition. Unlike conventional models that exhibit spectral bias toward low frequencies, our FrNFO employs fractional-order convolutions to capture both high and low-frequency dynamics, achieving approximately 10% improvement in F1-score and sensitivity over state-of-the-art baselines. The FrNFO enables the extraction of instantaneous phase and amplitude representations that are particularly informative for preictal biomarker discovery and enhance out-of-distribution generalization. FAPEX further integrates structural state-space modeling and channelwise attention, allowing it to handle heterogeneous electrode montages. Evaluated across 12 benchmarks spanning species (human, rat, dog, macaque) and modalities (Scalp-EEG, SEEG, ECoG, LFP), FAPEX consistently outperforms 23 supervised and 10 self-supervised baselines under nested cross-validation, with gains of up to 15% in sensitivity on complex cross-domain scenarios. It further demonstrates superior performance in several external validation cohorts. To our knowledge, these establish FAPEX as the first epilepsy model to show consistent superiority in SASP, offering a promising solution for discovering epileptic biomarker evidence supporting the existence of a distinct and identifiable preictal state and clinical translation.