Precise staging of diabetic retinopathy (DR) is crucial but challenging in real-world settings due to the limited availability of tabletop retinal imaging and inconsistencies in pictures captured by handheld fundus cameras, which reduces the effectiveness of deep learning. This study introduces a robust deep learning pipeline for noisy, imbalanced, and heterogeneous fundus datasets acquired from portable handheld devices. The proposed approach enhances pathological feature visibility by an improved image enhancement pipeline that combines fractional-order anisotropic diffusion, CLAHE, and unsharp masking, improving image quality before classification. Transfer learning with EfficientNet-B3 is utilized for model training and optimizing it using a fractional-order optimizer that adaptively interpolates between first and higher-order memory-augmented descent to stabilize training. On held-out test data, the proposed fractional-order training achieves consistent gains in staging and DR detection relative to standard RMSProp, SGD Nestrov, and Adam baselines. Ablations show that the fractional memory parameter provides a tunable bias-variance trade-off. The proposed pipeline achieves 92.37% accuracy and 88.56% F1-score for 2-class, and 90.51% accuracy and 88.37% F1-score for 3-class classification of the mBRSET dataset. These results suggest that fractional optimization can improve robustness and equity of DR screening models in real-world settings.