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Fractional Calculus and Applied Analysis

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Volume 19, Issue 2


On a Legendre Tau method for fractional boundary value problems with a Caputo derivative

Kazufumi Ito / Bangti Jin / Tomoya Takeuchi
Published Online: 2016-05-04 | DOI: https://doi.org/10.1515/fca-2016-0019


In this paper, we revisit a Legendre-tau method for two-point boundary value problems with a Caputo fractional derivative in the leading term, and establish an L2 error estimate for smooth solutions. Further, we apply the method to the Sturm-Liouville problem. Numerical experiments indicatethat for the source problem, it converges steadily at an algebraic rate even for nonsmooth data, and the convergence rate enhances with problem data regularity, whereas for the Sturm-Liouville problem, it always yields excellent convergence for eigenvalue approximations.

Key Words and Phrases: Caputo fractional derivative; Legendre tau method; error estimates; eigenvalue approximation

MSC 2010: Primary 65N35; Secondary 65N15, 34B10


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About the article

Received: 2015-02-13

Revised: 2015-09-01

Published Online: 2016-05-04

Published in Print: 2016-04-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 19, Issue 2, Pages 357–378, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0019.

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