期刊
ADVANCES IN DIFFERENCE EQUATIONS
卷 -, 期 -, 页码 -出版社
SPRINGER
DOI: 10.1186/s13662-017-1369-x
关键词
analytical solution; Caputo fractional derivative; Riesz fractional derivative; multi-term fractional diffusion equation; multivariate Mittag-Leffler function
The present paper deals with the Cauchy problem for the multi-term time-space fractional diffusion equation in one dimensional space. The time fractional derivatives are defined as Caputo fractional derivatives and the space fractional derivative is defined in the Riesz sense. Firstly the domain of the fractional Laplacian is extended to a Banach space. Then the analytical solutions are established by using the Luchko theorem and the multivariate Mittag-Leffler function.
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