Inverse problem of determining an order of the Caputo time-fractional derivative for a subdiffusion equation

Abstract

Abstract An inverse problem for determining the order of the Caputo time-fractional derivative in a subdiffusion equation with an arbitrary positive self-adjoint operator A with discrete spectrum is considered. By the Fourier method it is proved that the value of ∥ A ⁢ u ⁢ ( t ) ∥ {\|Au(t)\|} , where u ⁢ ( t ) {u(t)} is the solution of the forward problem, at a fixed time instance recovers uniquely the order of derivative. A list of examples is discussed, including linear systems of fractional differential equations, differential models with involution, fractional Sturm–Liouville operators, and many others.