Time-fractional radial diffusion in a sphere

The radial diffusion in a sphere of radius R is described using time-fractional diffusion equation. The Caputo fractional derivative of the order 0 <alpha < 2 is used. The Laplace and finite sin-Fourier transforms are employed. The solution is written in terms of the Mittag-Leffler functions. For the first and second time-derivative terms, the obtained solutions reduce to the solutions of the ordinary diffusion and wave equations. Several examples of signaling, source and Cauchy problems are presented. Numerical results are illustrated graphically.