In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on th...

Diffuse optical tomography is an emerging technique for non-invasively measuring in vivo tissue optical properties. The next generation of DOT time domain imaging systems will allow researchers to create three-dimensional (3D) images of blood volume and oxygenation with unprecedented spatial resolution. We consider common semi-infinite and slab geometries, in the Born approximation to the diffu...