Backward problems in time for fractional diffusion-wave equation

In this article, for a time-fractional diffusion-wave equation $\pppa u(x,t) = -Au(x,t)$,$0<t<T$withfractionalorder$\alpha \in (1,2)$, we consider the backward problem in time: determine $u(\cdot ,t)$, $0<t<T$ by $u(\cdot ,T)$ and ${\text{ppp}}_{t}u(\cdot ,T)$. We proved that there exists a countably infinite set $\mathrm{\Lambda }\in (0,\mathrm{\infty })$ with a unique accumulation point $0$ such that the backward problem is well-posed for $T\in ̸\mathrm{\Lambda }$.