Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4): 1446-1468.doi: 10.1007/s42967-022-00211-3

• ORIGINAL PAPERS • Previous Articles     Next Articles

Three Kinds of Discrete Formulae for the Caputo Fractional Derivative

Zhengnan Dong, Enyu Fan, Ao Shen, Yuhao Su   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2022-06-30 Revised:2022-08-07 Published:2023-12-16
  • Contact: Enyu Fan,E-mail:fanenyu@shu.edu.cn E-mail:fanenyu@shu.edu.cn

Abstract: In this paper, three kinds of discrete formulae for the Caputo fractional derivative are studied, including the modified L1 discretisation for α ∈ (0, 1), and L2 discretisation and L2C discretisation for α ∈ (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.

Key words: Caputo fractional derivative, Modified L1 discretisation, L2 discretisation, L2C discretisation, Truncation error

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