An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, \(\alpha \) and \(\alpha _m\), it is assumed \(1<\alpha <2\) and \(\alpha -\alpha _m\le 1\). Subordination principle with respect to the corresponding single-term time-fractional wave equation of order \(\alpha \) is deduced. Injectivity of the integral transform, defined by the subordination relation, is established. The subordination identity is used to prove uniqueness for a coefficient inverse problem for the multi-term equation, based on an analogous property for the related single-term one. In addition, the subordination relation is applied for deriving a regularity estimate.

考虑有界域上多项时间分数阶波动方程的初边值问题。对于所涉及的 Caputo 分数时间导数的最大和最小阶，\(\alpha \)和\(\alpha _m\)，假设\(1<\alpha <2\)和\(\alpha -\阿尔法_m\le 1\)。推导了对应的\(\alpha \)阶单项时间分数阶波动方程的从属原理。建立了由从属关系定义的积分变换的内射性。从属恒等式用于基于相关单项方程的类似性质来证明多项方程的系数反问题的唯一性。此外，应用从属关系来推导规律性估计。