Volume 18, Issue 4
An Effective Algorithm for Computing Fractional Derivatives and Application to Fractional Differential Equations

Minling Zhang, Fawang Liu & Vo Anh

Int. J. Numer. Anal. Mod., 18 (2021), pp. 458-480.

Published online: 2021-05

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  • 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.

  • Keywords

Riemann-Liouville derivative, Caputo fractional derivative, Riesz fractional derivative, spectral collocation method, fractional differentiation matrix.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-458, author = {Zhang , Minling and Liu , Fawang and Anh , Vo}, title = {An Effective Algorithm for Computing Fractional Derivatives and Application to Fractional Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19116.html} }
TY - JOUR T1 - An Effective Algorithm for Computing Fractional Derivatives and Application to Fractional Differential Equations AU - Zhang , Minling AU - Liu , Fawang AU - Anh , Vo JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 458 EP - 480 PY - 2021 DA - 2021/05 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19116.html KW - Riemann-Liouville derivative, Caputo fractional derivative, Riesz fractional derivative, spectral collocation method, fractional differentiation matrix. AB -

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.

Minling Zhang, Fawang Liu & VoAnh. (2021). An Effective Algorithm for Computing Fractional Derivatives and Application to Fractional Differential Equations. International Journal of Numerical Analysis and Modeling. 18 (4). 458-480. doi:
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