The fractional derivative models with time-varying viscosity have been used in characterizing creep or relaxation properties of different viscoelastic material, and many combination models were presented using the Boltzmann superposition principle. However, those models defined as initial ones in this manuscript usually ignored the initial loading ramp, and the ideal-loading condition is commonly assumed as a step function in modeling. The real-loading conditions of tested samples are usually a ramp load followed by constant stress or strain. The difference in loading conditions between the theoretical modeling and experimental procedure strongly influences the models’ rheological property characterization and parameter determination. It is especially the case for the fractional derivative model due to its memory or history-dependent characters, even though the ramp time is short compared with the total experimental time. An application example of the Maxwell model with time-varying viscosity Scott–Blair model (TVSM) shows that the initial loading ramp has a strong influence. To solve this problem, the authors propose modified models of TVSM based on real-loading conditions. The relative errors between initial and modified models are presented. In addition, a history-dependent optimization algorithm for parameter determination is proposed. Three sets of polymer experimental data are employed to suggest that the fitting results of models disregarding initial ramp loads are unreliable. The modified model should be used for characterizing rheological behavior, as this leads to obtaining the best fitting results even for a short experimental time.

具有随时间变化的粘度的分数阶导数模型已用于表征不同粘弹性材料的蠕变或松弛特性，并且使用玻尔兹曼叠加原理提出了许多组合模型。但是，在本手稿中定义为初始模型的那些模型通常会忽略初始加载斜率，并且理想加载条件通常被认为是建模中的阶跃函数。被测样品的实际载荷条件通常是斜坡载荷，然后是恒定的应力或应变。理论建模和实验步骤之间的加载条件差异极大地影响了模型的流变特性表征和参数确定。对于分数导数模型，尤其是这种情况，因为它具有记忆或与历史相关的特征，即使斜坡时间与总实验时间相比也很短。带有随时间变化的粘度Scott-Blair模型（TVSM）的Maxwell模型的应用示例表明，初始加载斜率具有很大的影响力。为了解决这个问题，作者提出了基于实际载荷条件的TVSM修正模型。提出了初始模型和修改模型之间的相对误差。此外，提出了一种基于历史的参数确定优化算法。使用三组聚合物实验数据表明，忽略初始斜升载荷的模型的拟合结果是不可靠的。修改后的模型应用于表征流变行为，因为即使在很短的实验时间内，这也可以获得最佳的拟合结果。