Fractional differential equations (FDEs), i.e. differential equations with derivatives of non-integer order, can describe certain experimental datasets more accurately than classic models and have found application in pharmacokinetics (PKs), but wider applicability has been hindered by the lack of appropriate software. In the present work an extension of NONMEM software is introduced, as a FORTRAN subroutine, that allows the definition of nonlinear mixed effects (NLME) models with FDEs. The new subroutine can handle arbitrary user defined linear and nonlinear models with multiple equations, and multiple doses and can be integrated in NONMEM workflows seamlessly, working well with third party packages. The performance of the subroutine in parameter estimation exercises, with simple linear and nonlinear (Michaelis–Menten) fractional PK models has been evaluated by simulations and an application to a real clinical dataset of diazepam is presented. In the simulation study, model parameters were estimated for each of 100 simulated datasets for the two models. The relative mean bias (RMB) and relative root mean square error (RRMSE) were calculated in order to assess the bias and precision of the methodology. In all cases both RMB and RRMSE were below 20% showing high accuracy and precision for the estimates. For the diazepam application the fractional model that best described the drug kinetics was a one-compartment linear model which had similar performance, according to diagnostic plots and Visual Predictive Check, to a three-compartment classic model, but including four less parameters than the latter. To the best of our knowledge, it is the first attempt to use FDE systems in an NLME framework, so the approach could be of interest to other disciplines apart from PKs.

分数阶微分方程（FDE），即具有非整数阶导数的微分方程，可以比经典模型更准确地描述某些实验数据集，并已在药代动力学（PK）中得到应用，但由于缺乏适当的软件，其更广泛的适用性受到阻碍。在目前的工作中，引入了 NONMEM 软件的扩展，作为 FORTRAN 子例程，它允许使用 FDE 定义非线性混合效应 (NLME) 模型。新的子程序可以处理任意用户定义的具有多个方程和多个剂量的线性和非线性模型，并且可以无缝集成到 NONMEM 工作流程中，与第三方软件包配合良好。通过模拟评估了参数估计练习中子程序的性能，以及简单的线性和非线性 (Michaelis-Menten) 分数 PK 模型，并提出了在地西泮真实临床数据集上的应用。在模拟研究中，我们对这两个模型的 100 个模拟数据集分别进行了模型参数估计。计算相对平均偏差（RMB）和相对均方根误差（RRMSE）以评估该方法的偏差和精度。在所有情况下，人民币和 RRMSE 均低于 20%，显示了估算的高度准确度和精度。对于地西泮应用，最能描述药物动力学的分数模型是单室线性模型，根据诊断图和视觉预测检查，该模型与三室经典模型具有相似的性能，但比后者少四个参数。据我们所知，这是在 NLME 框架中使用 FDE 系统的首次尝试，因此该方法可能会引起除了 PK 之外的其他学科的兴趣。