Exact solutions for fractional diffusion equation in a bounded domain with different boundary conditions

We give an analytical treatment of a time fractional diffusion equation with Caputo time-fractional derivative in a bounded domain with different boundary conditions. We use the Fourier method of separation of variables and Laplace transform method. The solution is obtained in terms of the Mittag-Leffler-type functions and complete set of eigenfunctions of the Sturm-Liouville problem. Such problems can be used in the context of anomalous diffusion in complex media, as well as for modeling voltammetric experiment in limiting diffusion space.