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

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  • Chen, Shanzhen
  • Jiang, Xiaoyun

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.

Suggested Citation

  • Chen, Shanzhen & Jiang, Xiaoyun, 2012. "Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3865-3874.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:15:p:3865-3874
    DOI: 10.1016/j.physa.2012.03.014
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    Cited by:

    1. Feng, Libo & Turner, Ian & Moroney, Timothy & Liu, Fawang, 2022. "An investigation of space distributed-order models for simulating anomalous transport in a binary medium," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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