This paper studies a time-fractional diffusion-wave equation with a linear source function. First, some stability results on parameters of the Mittag-Leffler functions are established. Then, we focus on studying the continuity of the solution of both the initial problem and the inverse initial value problems corresponding to the fractional-order in our main results. One of the difficulties encounteblack comes from estimating all constants independently of the fractional orders. Finally, we present some numerical results to confirm the effectiveness of our methods.

中文翻译：

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关于时间分数阶扩散波方程的分数阶的连续性

本文研究了具有线性源函数的时间分数阶扩散波方程。首先，建立了一些关于Mittag-Leffler函数参数的稳定性结果。然后，我们专注于研究与主要结果中的分数阶相对应的初始问题和逆初始值问题的解的连续性。遇到困难的困难之一是独立于分数阶来估计所有常数。最后，我们提出一些数值结果，以证实我们方法的有效性。