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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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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32 citations in Scopus
31 citations in Web of Science®
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ID Code: 51516
Item Type: Journal Article
Refereed: Yes
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: Crown Copyright © 2012 Published by Elsevier Ltd.
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, [Volume 64, Issue 10, (November 2012)]. DOI: 10.1016/j.camwa.2012.02.042
Deposited On: 10 Jul 2012 03:06
Last Modified: 05 Dec 2013 16:42

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