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This paper aims to feature new results on fixed-deviation stabilization and synchronization in neurodynamic systems of fractional order. This paper attempts to propose novel control algorithms that are based on linear-type discontinuous control, on the approach of auxiliary functions, and on fractional calculus to solve the problems of fixed-deviation stabilization and synchronization. This paper remains the focus of attention for stabilization and synchronization from the discontinuous control point of view; namely, the system under consideration is subject to discontinuous control. This paper shows that as long as some system-parameter-dependent conditions hold, the fixed-deviation stabilization and synchronization in fractional-order neurodynamic systems with communication delays can still be guaranteed, while good performance can be achieved even with heavy interference. Moreover, the fixed-deviation degree can be directly derived and estimated. Examples, together with their respective numerical simulations, show that the developing results are verifiable.