In the present paper, to fill the gap of the effect of singularity arising from multiple fractional derivatives on numerical analysis, the regularity and high order difference scheme for time fractional telegraph equations are taken into consideration. Firstly, the analytic solution is obtained by employing Laplace transform, and its regularity is then deduced. Secondly, by the technic of decomposition, the improved regularity of solution is derived. Furthermore, to overcome the weak singularity and enhance convergence precision, a second-order fitted scheme based on L2-\(1_\sigma \) approximation and order reduction method is applied to such problems, which is an improvement for the work [6]. Ultimately, examples are presented to verify the effectiveness of our theoretical results.

在本文中，为了填补多分数阶导数产生的奇点对数值分析影响的空白，考虑了时间分数电报方程的规律性和高阶差分方案。首先，采用拉普拉斯变换得到解析解，然后推导其规律性。其次，通过分解技术，推导出改进的溶液规则性。此外，为了克服弱奇异性并提高收敛精度，对此类问题应用了基于 L2-\（1_\sigma \） 近似和降阶方法的二阶拟合方案，这是对工作的改进 [6]。最后，提出了一些例子来验证我们的理论结果的有效性。