Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

Ye, H., Liu, F., Anh, V., & Turner, I. (2014) Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations. Applied Mathematics and Computation, 227, pp. 531-540.

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Abstract

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

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15 citations in Scopus
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ID Code: 82658
Item Type: Journal Article
Refereed: Yes
Keywords: Multi-term time–space fractional differential equation Riesz–Caputo fractional derivative Maximum principle Predictor–corrector method L1/L2-approximation method
DOI: 10.1016/j.amc.2013.11.015
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Elsevier Inc.
Copyright Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes 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 Applied Mathematics and Computation, Volume 227, 15 January 2014, Pages 531–540 DOI 10.1016/j.amc.2013.11.015
Deposited On: 22 Mar 2015 23:54
Last Modified: 16 Jan 2016 07:54

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