Uniqueness and Existence for Inverse Problem of Determining an Order of Time-Fractional Derivative of Subdiffusion Equation

An inverse problem for determining the order of time-fractional derivative in a nonhomogeneous subdiffusion equation with an arbitrary elliptic differential operator with constant coefficients in N-dimensional torus is considered. Using the classical Fourier method it is proved, that the value of the solution at a fixed time instant as the observation data recovers uniquely the order of fractional derivative. Generalization to an arbitrary N-dimensional domain and to elliptic operators with variable coefficients is considered.