Spectral methods for tempered fractional differential equations

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouville operator in the sense of the norm. Spec- tral Galerkin and Petrov-Galerkin methods for tempered fractional advection problems and tempered fractional diffusion problems can be developed as the classical spectral Galerkin and Petrov-Galerkin methods. Error analysis is provided and numerically confirmed for the tempered fractional advection and diffusion problems.


Published in:
Mathematics of Computation
Year:
2016
ISSN:
0025-5718
Keywords:
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 Record created 2016-04-03, last modified 2018-12-03

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