Coefficient inverse problem for a fractional diffusion equation

In this paper, we consider an initial/boundary value problem for a fractional diffusion equation in a bounded domain Omega: partial derivative(alpha)(t)u = Delta u + p(x)u where partial derivative(alpha)(t) is the Caputo derivative and 0 < alpha < 2, alpha not equal 1. We discuss an inverse problem of determining spatial coefficient p(x), x is an element of Omega and/or order alpha of the fractional derivative by data u vertical bar(omega x( 0,T)), where omega subset of Omega is a sub-domain. Our main result is the uniqueness under conditions where the initial value is positive and omega is a neighbourhood of partial derivative Omega. The proof is done by transforming the solution u to the solution of the wave equation.