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 - <p style="text-align: justify;">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 $O$($J$<sup>2</sup>$N$) 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.</p>