Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 351, Issue 1, Pages 218-223Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2008.10.018
Keywords
Caputo-Dzherbashyan fractional derivative; Time-fractional diffusion equation; Initial-boundary-value problems; Maximum principle; Uniqueness theorem
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In the paper, a maximum principle for the generalized time-fractional diffusion equation over an open bounded domain G x (0. T). G subset of R-n is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Caputo-Dzherbashyan fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the generalized time-fractional diffusion equation possesses at most one classical solution and this Solution continuously depends on the initial and boundary conditions. (c) 2008 Elsevier Inc. All rights reserved.
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