The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers’ equations. A new parameter ${\sigma }_t$ is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter ${\sigma }_t$ and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method.

中文翻译：

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用于求解复阶分数阶Burgers方程的非标准有限差分方法。

这项工作的目的是为Burgers方程的一阶复数分数非线性一维问题提供数值处理。新参数${\sigma }_{Ť}$为了与物理模型问题相一致，提出了。该参数表征方程中分数结构的存在。参数之间的关系${\sigma }_{Ť}$然后导出时间导数复数阶。提出了一种使用加权平均非标准有限差分离散化的无条件稳定数值格式。研究了该方法的稳定性。数值仿真证明了该方法的可靠性。