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Discretised general fractional derivative

Author

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  • Fan, Enyu
  • Li, Changpin
  • Stynes, Martin

Abstract

A generalised fractional derivative (the ψ-Caputo derivative) is studied. Generalisations of standard discretisations are constructed for this derivative: L1, L1-2, L2-1σ for derivatives of order α∈(0,1), and L2, H2N2, L21 for derivatives of order α∈(1,2). These new discretisations extend known results for the standard Caputo derivative, the Caputo–Hadamard derivative, etc. Numerical examples are given to demonstrate their performance.

Suggested Citation

  • Fan, Enyu & Li, Changpin & Stynes, Martin, 2023. "Discretised general fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 501-534.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:501-534
    DOI: 10.1016/j.matcom.2023.01.030
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    Keywords

    ψ-Caputo derivative; L1 discretisation; L1-2 discretisation; L2-1σ discretisation; L2 discretisation; H2N2 discretisation; L21 discretisation; Truncation error;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior
    • L21 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Business Objectives of the Firm

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