This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

中文翻译：

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新微管传输线模型的大量孤子解决方案：分数比较

本文在 Atangana-Baleanu 和 beta 导数的意义上介绍了一种新的分数电微管传输线模型，以理解控制系统的非线性动力学。这种结构拥有细胞过程生物学中最重要的部分之一，并且分数参数结合了微管中的记忆效应。此外，微管在细胞运动、信号传导和细胞内运输方面极为有益。新的扩展直接代数方法是一种用于提取孤子解的引人注目且有说服力的积分方案。检索到的解包括暗、亮和奇异孤子。该模型在展示非线性系统中的波传输方面发挥了重要作用。所提出的方法的新颖性和优势通过将其应用于该模型来描绘，其动态行为由 3D 和 2D 图描绘。本文还对不同分数参数值下的两种分数导数和敏感性分析图进行了比较研究。