期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 207, 期 2, 页码 245-257出版社
ELSEVIER
DOI: 10.1016/j.cam.2006.10.014
关键词
sub-diffusion; fractional derivatives; Mellin-Barnes integrals; Mittag-Leffler functions; fox-wright functions; integral transforms
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales related to the distribution of the fractional orders. The results of the time fractional diffusion equation of a single order are also recalled and then re-obtained from the general theory. (C) 2006 Elsevier B.V. All rights reserved.
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