Abstract In this paper, variable order Burgers' equations with proportional delays in time and space are studied. The variable order derivatives are defined in the sense of Atangana and Baleanu. Two types of variable order Atangana and Baleanu definitions are presented here. The nonstandard weighted average finite difference method is developed to study numerically the proposed models problem in one and two dimensional. Moreover, the stability analysis and truncation error are analyzed. Two test examples with proportional delays are given to characterizing the memory property of the proposed models. It is found that the proposed technique can be applied to study such variable-order fractional equations simply and effectively.

中文翻译：

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两类具有比例时滞的变阶Burgers方程的数值研究

摘要 本文研究了时空成比例时滞的变阶Burgers方程。变阶导数是在 Atangana 和 Baleanu 的意义上定义的。这里介绍了两种类型的可变阶 Atangana 和 Baleanu 定义。开发了非标准加权平均有限差分方法来数值研究一维和二维模型问题。此外，还对稳定性分析和截断误差进行了分析。给出了两个具有比例延迟的测试示例来表征所提出模型的记忆特性。发现所提出的技术可以简单有效地应用于研究此类变阶分数方程。