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

作者：Chen Shanzhen; Jiang Xiaoyun^*

来源：Physica A: Statistical Mechanics and Its Applications , 2012, 391(15): 3865-3874.

DOI：10.1016/j.physa.2012.03.014

• Fractional partial differential equation
• Multi-layer annulus
• Finite integral transform
• Mittag-Leffler function

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.

• 出版日期2012-8-1
• 单位山东大学