Uniqueness and Existence for Inverse Problem of Determining an Order of Time-Fractional Derivative of Subdiffusion Equation
Ravshan AshurovInstitute of Mathematis, Academy of Science of Uzbekistan, 100170, Tashkent, UzbekistanYusuf FayzievNational University of Uzbekistan, Students Town, 700174, Tashkent, Uzbekistan
ABI
Abstract
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.