Three Kinds of Discrete Formulae for the Caputo Fractional Derivative
Zhengnan Dong , Enyu Fan , Ao Shen , Yuhao Su
Communications on Applied Mathematics and Computation ›› 2022, Vol. 5 ›› Issue (4) : 1446 -1468.
Three Kinds of Discrete Formulae for the Caputo Fractional Derivative
In this paper, three kinds of discrete formulae for the Caputo fractional derivative are studied, including the modified L1 discretisation for $\alpha \in (0,1)$, and L2 discretisation and L2C discretisation for $\alpha \in (1,2)$. The truncation error estimates and the properties of the coefficients of all these discretisations are analysed in more detail. Finally, the theoretical analyses are verified by the numerical examples.
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