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The backward problem for subdiffusion equation with the fractionalRiemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positiveself-adjoint operator A is considered. This problem is ill-posed in the senseof Hadamard due to the lack of stability of the solution. Nevertheless, we willshow that if we consider sufficiently smooth current information, then thesolution exists and it is unique. Using this result, we study the inverseproblem of initial value identification for subdiffusion equation. The resultsobtained differ significantly from the corresponding results for the classicaldiffusion equation (i.e. ? = 1) and even for the subdiffusion equation with theCaputo derivative. A list of examples of operator A is discussed, includinglinear systems of fractional differential equations, differential models withinvolution, fractional Sturm-Liouville operators, and many others.

On the backward problems in time for time-fractional subdiffusion equations