Grünwald–Letnikov Fractional Ensemble with α-Specific Power Weighting for Multi-Cancer Classification

Standard ensemble classifiers assign weights based on performance over a single feature space, leaving multi-scale fractional representations unexplored as a tabular augmentation strategy. This study proposes the FRAE (Fractional-order Recalibrated Adaptive Ensemble) framework, which applies Grünwald–Letnikov (GL) derivatives at four memory orders as tabular feature augmentation and couples each view’s memory order to its ensemble weight via an α-specific power exponent. FRAE was evaluated on three open-access cancer datasets—WAW-TACE HCC (n = 198), Ye Prostate Cancer (C1 n = 298; C2 n = 300, external), and HANCOCK HNSCC (n = 763)—against nine baselines under 5-fold stratified cross-validation, with ablation across ten configurations. FRAE ranks first by MCC in D2 (0.587 vs. CAWPE 0.563) and second in D1 and D3, with the highest sensitivity in D3 (0.766). Ablation confirms that GL feature augmentation, not weight allocation, is the primary performance driver, contributing a directionally consistent AUC increment of 0.82–1.41 percentage points across all three tasks. On the external cohort, FRAE achieves AUC = 0.8305 [95% CI: 0.7772, 0.8739], ranking first by F1 and NPV, and tied for first by MCC among ten models, though confidence intervals overlap across all model pairs. Multi-institutional prospective validation remains the necessary next step.