In this paper, we construct the Bäcklund transformations and the super-position formulas to the constant coefficients local fractional Riccati equation for the first time. Next, by means of the Bäcklund transformations and seed solutions which have been known in [X. J. Yang et al., Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fundam. Inform. 151(1–4) (2017) 409–417], we can get a class of exact solutions to the third-order modified KdV equation on the fractal set. These new type solutions can assist us to review different nonlinear phenomena better, which had been modeled via local fractional derivative.

中文翻译：

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研究分形集上三阶修正 KDV 方程的新视角

本文首次构造了常系数局部分数Riccati方程的Bäcklund变换和叠加公式。接下来，通过 [XJ Yang 等人，局部分数非线性 Riccati 微分方程的不可微分解，Fundam.] 中已知的 Bäcklund 变换和种子解。通知。151（1-4）（2017）409-417]，我们可以得到分形集上三阶修正KdV方程的一类精确解。这些新型解决方案可以帮助我们更好地回顾不同的非线性现象，这些非线性现象是通过局部分数导数建模的。