Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

In this paper, analytical solutions to time-fractional partial differential equations in a multilayer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (alpha = 1), the Helmholtz equation (alpha -> 0) and the wave equation (alpha = 2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative. (C) 2012 Elsevier B.V. All rights reserved.