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.