In this paper, the stable analytical solutions’ accuracy of the nonlinear fractional nonlinear time–space telegraph (FNLTST) equation is investigated along with applying the trigonometric-quantic-B-spline (TQBS) method. This investigation depends on using the obtained analytical solutions to get the initial and boundary conditions that allow applying the numerical scheme in an easy and smooth way. Additionally, this paper aims to investigate the accuracy of the obtained analytical solutions after checking their stable property through using the properties of the Hamiltonian system. The considered model for this study is formulated by Oliver Heaviside in 1880 to define the advanced or voltage spectrum of electrified transmission, with day-to-day distances from the electrified communication or the application of electromagnetic waves. The matching between the analytical and numerical solutions is explained by some distinct sketches such as two-dimensional, scatter matrix, distribution, spline connected, bar normal, filling with two colors plots.

中文翻译：

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非线性分数时空电报方程的解析解与数值解

本文采用三角-量子-B-样条(TQBS)方法研究了非线性分数非线性时空电报(FNLTST)方程的稳定解析解的精度。这项研究依赖于使用获得的解析解来获得初始条件和边界条件，从而允许以简单和平滑的方式应用数值方案。此外，本文旨在通过使用哈密顿系统的性质检查其稳定性后，研究获得的解析解的准确性。本研究所考虑的模型由 Oliver Heaviside 于 1880 年制定，用于定义电气化传输的高级或电压频谱，以及与电气化通信或电磁波应用的日常距离。