The main idea of this paper is to search for all traveling wave solutions to an intrinsic fractional discrete nonlinear electrical transmission line, which plays a essential role in obtaining the new insights in nonlinear voltage dynamics. We first give a brief introduction how to transform the discrete system into a continuous one, which is described by a fractional-order partial differential equation. After that, this equation is handled by conformable fractional transformation and the complete discrimination system for polynomial method (CDSPM). By applying the advanced method, the whole of the exact traveling wave solutions emerged in existing articles are obtained, especially we obtain the solitary wave solutions and elliptic functions solutions which are hardly founded by other methods. Notably, the elliptic functions solutions in rational form are discovered for the first time. Finally, the electrical characteristics and the fractional nature are revealed via graphical represents. By the depicted graphs, we intuitively observe the existence of the phenomena for periodic wave and solitary wave, and the time-fractional derivative is proved do has important influence on the behaviors of the solutions. Considering the significance of the nonlinear electrical transmission line, the acquired results would have wide application in electrical engineering and nonlinear voltage dynamics, liking analyzing and predicting the complex voltage wave propagation phenomenon in realistic electrical transmission system.

本文的主要思想是搜索固有分数离散非线性电力传输线的所有行波解，这对于获得非线性电压动力学的新见解起着至关重要的作用。我们首先简要介绍如何将离散系统转化为连续系统，用分数阶偏微分方程描述。之后，该方程通过符合分数变换和多项式方法的完全判别系统（CDSPM）处理。应用先进的方法，得到了现有文章中出现的全部精确行波解，特别是得到了其他方法难以建立的孤立波解和椭圆函数解。尤其，首次发现了有理形式的椭圆函数解。最后，通过图形表示揭示电气特性和分数性质。通过绘制的图形，我们直观地观察到周期波和孤立波现象的存在，证明时间分数阶导数对解的行为有重要影响。考虑到非线性输电线路的重要性，所获得的结果将在电气工程和非线性电压动力学方面具有广泛的应用，例如分析和预测现实输电系统中复杂的电压波传播现象。电气特性和分数性质通过图形表示。通过绘制的图形，我们直观地观察到周期波和孤立波现象的存在，证明时间分数阶导数对解的行为有重要影响。考虑到非线性输电线路的重要性，所获得的结果将在电气工程和非线性电压动力学方面具有广泛的应用，例如分析和预测现实输电系统中复杂的电压波传播现象。电气特性和分数性质通过图形表示。通过绘制的图形，我们直观地观察到周期波和孤立波现象的存在，证明时间分数阶导数对解的行为有重要影响。考虑到非线性输电线路的重要性，所获得的结果将在电气工程和非线性电压动力学方面具有广泛的应用，例如分析和预测现实输电系统中复杂的电压波传播现象。