Abstract We consider a class of a generalized time-fractional telegraph equations. The existence of a weak solution of the corresponding initial-boundary value problem has been proved. A finite difference scheme approximating the problem is proposed, and its stability is proved. An estimate for the rate of convergence, in special discrete energetic Sobolev’s norm, is obtained. The theoretical results are confirmed by numerical examples.

中文翻译：

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广义时间分数电报方程的有限差分逼近

摘要 我们考虑一类广义时间分数电报方程。已经证明了相应初边值问题的弱解的存在性。提出了近似该问题的有限差分格式，并证明了其稳定性。获得收敛速度的估计值，在特殊离散能量 Sobolev 范数中。理论结果得到数值算例的证实。