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Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations

by and *,†
Department of Physical, Mathematical and Engineering, University of Chester, Chester CH1 4BJ, UK
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Sotiris K. Ntouyas
Foundations 2022, 2(4), 839-861; https://doi.org/10.3390/foundations2040057
Received: 28 August 2022 / Revised: 12 September 2022 / Accepted: 13 September 2022 / Published: 22 September 2022
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
We consider a predictor–corrector numerical method for solving Caputo–Hadamard fractional differential equation over the uniform mesh logtj=loga+logtNajN,j=0,1,2,,N with a1, where loga=logt0<logt1<<logtN=logT is a partition of [loga,logT]. The error estimates under the different smoothness properties of the solution y and the nonlinear function f are studied. Numerical examples are given to verify that the numerical results are consistent with the theoretical results. View Full-Text
Keywords: predictor–corrector method; Caputo–Hadamard fractional derivative; uniform meshes; error estimates; Adams–Bashforth–Moulton method; smoothness properties; error estimates predictor–corrector method; Caputo–Hadamard fractional derivative; uniform meshes; error estimates; Adams–Bashforth–Moulton method; smoothness properties; error estimates
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MDPI and ACS Style

Green, C.W.H.; Yan, Y. Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations. Foundations 2022, 2, 839-861. https://doi.org/10.3390/foundations2040057

AMA Style

Green CWH, Yan Y. Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations. Foundations. 2022; 2(4):839-861. https://doi.org/10.3390/foundations2040057

Chicago/Turabian Style

Green, Charles Wing Ho, and Yubin Yan. 2022. "Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations" Foundations 2, no. 4: 839-861. https://doi.org/10.3390/foundations2040057

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