Precise, generalizable subject-agnostic seizure prediction (SASP) remains a fundamental challenge due to the intrinsic complexity and significant spectral variability of electrophysiologial signals across individuals and recording modalities. We propose \model{FAPEX}, a novel architecture that introduces a learnable \emph{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 \emph{instantaneous phase and amplitude representations} that are particularly informative for preictal biomarker discovery and enhance out-of-distribution generalization. \model{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), \model{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 \model{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 for and clinical translation.