  In this work, we rigorously investigate the robustness of graph neural
fractional-order differential equation (FDE) models. This framework extends
beyond traditional graph neural (integer-order) ordinary differential equation
(ODE) models by implementing the time-fractional Caputo derivative. Utilizing
fractional calculus allows our model to consider long-term memory during the
feature updating process, diverging from the memoryless Markovian updates seen
in traditional graph neural ODE models. The superiority of graph neural FDE
models over graph neural ODE models has been established in environments free
from attacks or perturbations. While traditional graph neural ODE models have
been verified to possess a degree of stability and resilience in the presence
of adversarial attacks in existing literature, the robustness of graph neural
FDE models, especially under adversarial conditions, remains largely
unexplored. This paper undertakes a detailed assessment of the robustness of
graph neural FDE models. We establish a theoretical foundation outlining the
robustness characteristics of graph neural FDE models, highlighting that they
maintain more stringent output perturbation bounds in the face of input and
graph topology disturbances, compared to their integer-order counterparts. Our
empirical evaluations further confirm the enhanced robustness of graph neural
FDE models, highlighting their potential in adversarially robust applications.
