  A standard inverse problem is to determine a source which is supported in an
unknown domain $D$ from external boundary measurements. Here we consider the
case of a time-dependent situation where the source is equal to unity in an
unknown subdomain $D$ of a larger given domain $\Omega$. Overposed measurements
consist of time traces of the solution or its flux values on a set of discrete
points on the boundary $\partial\Omega$. The case of a parabolic equation was
considered in [HettlichRundell:2001]. In our situation we extend this to cover
the subdiffusion case based on an anomalous diffusion model and leading to a
fractional order differential operator. We will show a uniqueness result and
examine a reconstruction algorithm. One of the main motives for this work is to
examine the dependence of the reconstructions on the parameter $\alpha$, the
exponent of the fractional operator which controls the degree of anomalous
behaviour of the process. Some previous inverse problems based on fractional
diffusion models have shown considerable differences between classical Brownian
diffusion and the anomalous case.
