Arterial compliance is a vital determinant of the ventriculo-arterial coupling dynamic. Its variation is detrimental to cardiovascular functions and associated with heart diseases. Accordingly, assessment and measurement of arterial compliance are essential in the diagnosis and treatment of chronic arterial insufficiency. Recently, experimental and theoretical studies have recognized the power of fractional calculus to perceive viscoelastic blood vessel structure and biomechanical properties. This paper presents five fractional-order model representations to describe the dynamic relationship between the aortic blood pressure input and blood volume. Each configuration incorporates a fractional-order capacitor element (FOC) to lump the apparent arterial compliance's complex and frequency dependence properties. FOC combines both resistive and capacitive attributes within a unified component, which can be controlled through the fractional differentiation order factor, α. Besides, the equivalent capacitance of FOC is by its very nature frequency-dependent, compassing the complex properties using only a few numbers of parameters. The proposed representations have been compared with generalized integer-order models of arterial compliance. Both models have been applied and validated using different aortic pressure and flow rate data acquired from various species such as humans, pigs, and dogs. The results have shown that the fractional-order framework is able to accurately reconstruct the dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. It seems that this new paradigm confers a prominent potential to be adopted in clinical practice and basic cardiovascular mechanics research.