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

Abstract

The inverse problem of determining the order of the fractional RiemannLiouville derivative with respect to time in the subdiffusion 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 ||u(t)|| of the solution at a fixed time instance recovers uniquely the order of derivative. A list of examples is discussed, including a linear system of fractional differential equations, differential models with involution, fractional Sturm-Liouville operators, and many others. AMS 2000 Mathematics Subject Classifications : Primary 35R11; Secondary 74S25.