FrFNO: Injecting the analytic Mittag-Leffler propagator into a resolution-robust neural operator for space-time fractional PDEs

Fractional partial differential equations combine memory-dependent time derivatives with nonlocal fractional Laplacians, making repeated solution under varying parameters computationally expensive. The Fractional Fourier Neural Operator (FrFNO) addresses this by injecting the analytic Mittag-Leffler propagator into the neural operator architecture, enabling it to capture the dominant linear fractional evolution without relearning from scratch. This conditional operator provides resolution-robust predictions for fractional PDEs across different fractional orders, initial conditions, and diffusivity fields.