Inverse problem of determining an order of the Riemann-Liuville time-fractional derivative

Abstract

The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using the classical Fourier method it is proved, that the value of the norm jju(t)jj of the solution at a_xed time instance recovers uniquely the order of derivative. A list of examples is discussed, including a linear system of fractional di_erential equations, di_erential models with involution, fractional Sturm-Liouville operators, and many others.