Discretised general fractional derivative

Enyu Fan, Changpin Li and Martin Stynes

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 501-534

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.

Keywords: ψ-Caputo derivative; L1 discretisation; L1-2 discretisation; L2-1σ discretisation; L2 discretisation; H2N2 discretisation; L21 discretisation; Truncation error (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:501-534

DOI: 10.1016/j.matcom.2023.01.030

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