Atrial fibrillation (AF) is the most common arrhythmia within the clinical context. Advanced stages of the AF involve several difficulties in its management and treatment. This occurs mostly because the initiation and perpetuation mechanisms of the AF are still not fully understood. Cardiac scientific computation has become an important tool in researching the underlying mechanisms of the AF. In this work, an equation of action potential propagation that implements fractional order derivatives is used to model the atrial dynamics. The fractional derivative order represents the structural heterogeneities of the atrial myocardium. Using such mathematical operator, the Courtemanche and Maleckar human atrial electrophysiological models, during healthy and AF conditions, are assessed. The results indicate that, through the fractional order variations, there are electrophysiological properties whose behavior do not depend on the cellular model or physiological conditions. On the other hand, there are properties whose behavior under distinct values of the fractional order, are specific to the cellular model and to the physiological condition and they can be characterized quantitatively and qualitatively. Therefore, the fractional atrial propagation model can be a useful tool for modeling a wide range of electrophysiological scenarios in both healthy and AF conditions. © 2019, Springer Nature Switzerland AG.