Variational formulation of problems involving fractional order differential operators

but the solutions are less regular, whereas that for the Caputo case involves different test and trial spaces. The numerical analysis of these problems requires the so-called shift theorems which show that the solutions of the variational problem are more regular. The regularity pickup enables one t...

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Bibliographic Details
Published in:Mathematics of computation 2015-11, Vol.84 (296), p.2665-2700
Main Authors: JIN, BANGTI, LAZAROV, RAYTCHO, PASCIAK, JOSEPH, RUNDELL, WILLIAM
Format: Article
Language:English
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Summary:but the solutions are less regular, whereas that for the Caputo case involves different test and trial spaces. The numerical analysis of these problems requires the so-called shift theorems which show that the solutions of the variational problem are more regular. The regularity pickup enables one to establish convergence rates of the finite element approximations. The analytical theory is then applied to the Sturm-Liouville problem involving a fractional derivative in the leading term. Finally, extensive numerical results are presented to illustrate the error estimates for the source problem and eigenvalue problem.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/2960