Inverse problems of determining an order of fractional Riemann-Liouville time-fractional derivative for the subdiffusion equation in RN

An initial-boundary value problem for the subdiffusion equation with an elliptic operator A(D) in RN is studied in the article. Existence and uniqueness theorems for the problem under study are proved by the Fourier method. Considering the order of the Riemann-Liouville time-fractional derivative as an unknown parameter, an inverse problem of determining this parameter is investigated. Likewise, the initial-boundary value problem was considered in the case of replacing the operator A(D) with its power Aσ.Then, existence and uniqueness theorems were proved for the solution of the inverse problem of determining the order of the fractional derivative and the power σ.