The fractional derivative concept to treat non-isothermal solid state thermal decomposition was employed in this work. Simulated data were compared with the exact solutions for the method validation. Calculated fractional kinetics data for four heating rates were initially considered and the Kissinger-Akahira-Sunose (KAS) method demonstrate that, although the activation energy is not retrieved, it can be useful to determine a single or multistep process. Experimental thermal decomposition data of lumefantrine heated at 5, 10 ,15, and 20 ^oC min^− 1 were fitted for a single-step process. The kinetic parameters were retrieved for integer and fractional kinetics, considering some ideal and general models. Application of the KAS method to these data demonstrated an activation energy dependent on the conversion rate, indicating a multistep process. Five data subintervals were fitted separately using the general model with variable derivative order. It was found a process that occours with integer order derivative until α = 0.3 and fractional order for α > 0.3 with combination of simultaneous reactions, since the parameters do not correspond to any ideal model. The determined activation energies showed the same increasing behavior observed in the KAS approach. The results for multistep process presented an error 10² times smaller if compared with the best result, considering a single-step process. Therefore, the fractional kinetic model presents a powerful extension to the usual thermal data analysis.

中文翻译：

---

热分析中的分数动力学：应用于麻黄素的热分解。

在这项工作中采用分数导数概念来处理非等温固态热分解。将模拟数据与用于方法验证的确切解决方案进行比较。最初考虑了四个加热速率的计算分数动力学数据，并且Kissinger-Akahira-Sunose（KAS）方法证明，尽管未获取活化能，但对确定单步或多步过程可能有用。在5、10、15和20 ^o C min ^-1下加热的黄麻素的实验热分解数据适合单步过程。考虑一些理想模型和通用模型，获取了整数和分数动力学的动力学参数。将KAS方法应用于这些数据表明，活化能取决于转化率，表明该过程为多步过程。使用具有可变导数阶数的通用模型分别拟合了五个数据子间隔。由于参数不对应任何理想模型，因此发现了一个过程，该过程以整数阶导数出现，直到α = 0.3为止，而α > 0.3时存在分数阶，同时发生反应。所确定的活化能显示出在KAS方法中观察到的相同的增加行为。多步骤过程的结果显示错误10 ²如果考虑最佳步骤，则与单步执行过程相比，可以节省两倍的时间。因此，分数动力学模型为常规热数据分析提供了有力的扩展。