In this work, space-time fractal model about nonlinear KdV-Burgers–Kuramoto (NKBK) equation which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters has been put forward through coupling fractional complex transform (FCT) via local fractional derivative (LFD) for the first time. These measures are considered in the sense of local derivative operators. Analytical approximate solutions of the model are obtained by local fractional reduced differential transform method (LFRDTM). The obtained results related to physical phenomenon in Cantorian time-space reveal that the suggested project is easy to use and the calculation is more precise. The graphical representation of special solution of LFNKBK yields interesting and better physical consequences of NKBK with LFD.

中文翻译：

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局部分数微分算子内分形 KdV-Burgers-Kuramoto 方程的行波解

在这项工作中，通过局部分数导数耦合分数复数变换（FCT），提出了描述非线性物理现象并涉及不稳定性、耗散和色散参数的非线性KdV-Burgers-Kuramoto（NKBK）方程的时空分形模型。 （LFD）第一次。这些措施是在本地衍生运营商的意义上考虑的。该模型的解析近似解是通过局部分数缩减微分变换方法（LFRDTM）得到的。所获得的与康托利亚时空物理现象相关的结果表明，所提出的方案易于使用，计算更精确。LFNKBK 特殊解的图形表示产生了 NKBK 与 LFD 的有趣和更好的物理结果。