@Article{IJNAM-18-4,
author = {Zhang, Minling and Liu, Fawang and Vo, Anh},
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 = {<p style="text-align: justify;">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.<br/></p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-19116},
url = {https://global-sci.com/article/82991/an-effective-algorithm-for-computing-fractional-derivatives-and-application-to-fractional-differential-equations}
}