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Volume 17, Issue 2
A Finite Difference Scheme for Caputo-Fabrizio Fractional Differential Equations

Xu Guo, Yutian Li & Tieyong Zeng

Int. J. Numer. Anal. Mod., 17 (2020), pp. 195-211.

Published online: 2020-02

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  • Abstract

In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo–Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from $O$($J$2$N$) to $O$($JN$), and the corresponding storage will be cut down from $O$($JN$) to $O$($N$), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.

  • Keywords

Caputo–Fabrizio derivative, fractional differential equations, higher order scheme.

  • AMS Subject Headings

26A33, 35R11, 65N06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guoxu5861@gmail.com (Xu Guo)

liyutian@cuhk.edu.cn (Yutian Li)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-195, author = {Guo , XuLi , Yutian and Zeng , Tieyong}, title = {A Finite Difference Scheme for Caputo-Fabrizio Fractional Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {195--211}, abstract = {

In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo–Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from $O$($J$2$N$) to $O$($JN$), and the corresponding storage will be cut down from $O$($JN$) to $O$($N$), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13647.html} }
TY - JOUR T1 - A Finite Difference Scheme for Caputo-Fabrizio Fractional Differential Equations AU - Guo , Xu AU - Li , Yutian AU - Zeng , Tieyong JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 195 EP - 211 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13647.html KW - Caputo–Fabrizio derivative, fractional differential equations, higher order scheme. AB -

In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo–Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from $O$($J$2$N$) to $O$($JN$), and the corresponding storage will be cut down from $O$($JN$) to $O$($N$), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.

Guo , XuLi , Yutian and Zeng , Tieyong. (2020). A Finite Difference Scheme for Caputo-Fabrizio Fractional Differential Equations. International Journal of Numerical Analysis and Modeling. 17 (2). 195-211. doi:
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