Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
Jiang, H., Liu, F., Turner, I., & Burrage, K. (2012) Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Computers & Mathematics with Applications, 64(10), pp. 3377-3388.
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Abstract
Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited.
In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.
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| ID Code: | 51516 |
|---|---|
| Item Type: | Journal Article |
| Keywords: | Multi-term time-fractional diffusion equations, Multi-term time-fractional diffusion-wave equations, Multivariate Mittag-Leffler function, Separating of variables, Nonhomogeneous initial-boundary-value problems, Analytical solution |
| DOI: | 10.1016/j.camwa.2012.02.042 |
| ISSN: | 1873-7668 |
| Subjects: | Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) |
| Divisions: | Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty |
| Copyright Owner: | Copyright 2012 Elsevier |
| Copyright Statement: | This is the author's version of a work that was accepted for publication in Computers & Mathematics with Applications. Chanes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, [Vol. 64, No. 10, 2012] http://dx.doi.org/10.1016/j.camwa.2012.02.042 |
| Deposited On: | 10 Jul 2012 13:06 |
| Last Modified: | 16 May 2013 00:01 |
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