Nonlinear phenomena play an essential role in various field of natural sciences and engineering. In particular, the nonlinear chemical reactions are observed in various domains, as, for instance, in biological and chemical physics. For this reason, it is important to investigate the solution to this nonlinear phenomenon. This article investigates numerical solutions to a nonlinear oscillatory system called the Belousov–Zhabotinsky with Caputo fractional-time derivative. The simplified Noyes–Field fractional model reads

where \(\xi _1\) and \(\xi _2\) are the diffusing constants for the concentration p and w respectively, \(\gamma \) and \(\beta \) are given constants, \(\lambda \ne 1\) and \(\delta \) are positive parameters. The two iterative techniques used in this work are the fractional reduced differential transform method and q-homotopy analysis transform method. The outcomes using these two methods reveal an efficient numerical solution with high accuracy and minimal computations. Furthermore, to better understand the effect of the fractional order, we present the solution profiles which demonstrate the behavior of the obtained results.

非线性现象在自然科学和工程学的各个领域中起着至关重要的作用。特别地，例如在生物和化学物理学中，在各个领域中观察到非线性化学反应。因此，研究此非线性现象的解决方案很重要。本文研究了带有Caputo分数时间导数的非线性振荡系统Belousov–Zhabotinsky的数值解。简化的Noyes-Field分数模型读取

其中\（\ xi _1 \）和\（\ xi _2 \）分别是浓度p和w的扩散常数，\（\ gamma \）和\（\ beta \）被赋予常数\（\ lambda \ ne 1 \）和\（\ delta \）是正参数。这项工作中使用的两种迭代技术是分数缩减差分变换方法和q同伦分析变换方法。使用这两种方法的结果揭示了一种高效，高精度和最少计算量的数值解决方案。此外，为了更好地理解分数阶的影响，我们提供了解决方案配置文件，这些文件说明了所得结果的行为。