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

Shanzhen Chen and Xiaoyun Jiang

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 15, 3865-3874

Abstract: In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer 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 (α=1), the Helmholtz equation (α→0) and the wave equation (α=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.

Keywords: Fractional partial differential equation; Multi-layer annulus; Finite integral transform; Mittag-Leffler function (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:15:p:3865-3874

DOI: 10.1016/j.physa.2012.03.014

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