  The backward problem for subdiffusion equation with the fractional
Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive
self-adjoint operator A is considered. This problem is ill-posed in the sense
of Hadamard due to the lack of stability of the solution. Nevertheless, we will
show that if we consider sufficiently smooth current information, then the
solution exists and it is unique. Using this result, we study the inverse
problem of initial value identification for subdiffusion equation. The results
obtained differ significantly from the corresponding results for the classical
diffusion equation (i.e. ? = 1) and even for the subdiffusion equation with the
Caputo derivative. A list of examples of operator A is discussed, including
linear systems of fractional differential equations, differential models with
involution, fractional Sturm-Liouville operators, and many others.
