Determining the order of time and spatial fractional derivatives in a subdiffusion equation

The paper considers the initial-boundary value problem for equation Dtρu(x; t) + (−∆)σu(x; t) = 0, ρ; σ 2 (0; 1), in an N-dimensional domain Ω with a homogeneous Dirichlet condition. The fractional derivative is taken in the sense of Caputo. The main goal of the work is to solve the inverse problem of simultaneously determining two parameters: the order of the fractional derivative ρ and the degree of the Laplace operator σ. A new formulation and solution method for this inverse problem are proposed.