An Effective Algorithm for Computing Fractional Derivatives and Application to Fractional Differential Equations
Year: 2021
Author: Minling Zhang, Fawang Liu, Vo Anh
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 458–480
Abstract
In recent years, fractional differential equations have been extensively applied to
model various complex dynamic systems. The studies on highly accurate and efficient numerical
methods for fractional differential equations have become necessary. In this paper, an effective
recurrence algorithm for computing both the fractional Riemann-Liouville and Caputo derivatives
is proposed, and then spectral collocation methods based on the algorithm are investigated for
solving fractional differential equations. By the recurrence method, the numerical stability with
respect to $N$, the number of collocation points, can be improved remarkably in comparison with
direct algorithm. Its robustness ensures that a highly accurate spectral collocation method can
be applied widely to various fractional differential equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-19116
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 4 : pp. 458–480
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Riemann-Liouville derivative Caputo fractional derivative Riesz fractional derivative spectral collocation method fractional differentiation matrix.