fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations

ArXi:2605.16594v1 Announce Type: cross In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy for the Caputo fractional derivative of order $\beta \in (1,2)$. Building upon this foundation, we propose the fPINN-DeepONet framework, a novel approach that integrates operator learning with the $L_2$ approximation to efficiently solve fractional partial differential equations (FPDEs.