Normal diffusion has ⟨x²⟩ ∝ t. Anomalous diffusion breaks this: subdiffusion (⟨x²⟩ ∝ tᵅ, α<1) arises from power-law waiting times; superdiffusion from Lévy flights with infinite-variance step distributions. The fractional Fokker-Planck equation generalizes the diffusion equation via fractional time/space derivatives, capturing biological crowding, plasma transport, and financial volatility.