Backward problems in time for fractional diffusion-wave equation

In this article, for a time-fractional diffusion-wave equation partial derivative(alpha)(t)u(x, t) = -Au(x, t), 0 < t < T with fractional order alpha is an element of (1, 2), we consider the backward problem in time: determine u(., t), 0 < t < T by u(., T) and partial differential partial derivative(t)u(., T). We prove that there exists a countably infinite set Lambda subset of (0, infinity) with a unique accumulation point 0 such that the backward problem is well-posed for T is not an element of Lambda.