Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation

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, \(\alpha \) $\alpha$ and \(\alpha _m\) ${\alpha }_m$ , it is assumed \(1<\alpha <2\) $1<\alpha <2$ and \(\alpha -\alpha _m\le 1\) $\alpha -{\alpha }_m\le 1$ . Subordination principle with respect to the corresponding single-term time-fractional wave equation of order \(\alpha \) $\alpha$ 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.