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Detailed Error Analysis for a Fractional Adams Method on Caputo--Hadamard Fractional Differential Equations
Yan, Yubin Green, Charles
Yan, Yubin
Green, Charles
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2022-09-22
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Abstract
We consider a predictor--corrector numerical method for solving Caputo--Hadamard fractional differential equation over the uniform mesh $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \big ( \frac{j}{N} \big ), \, j=0, 1, 2, \dots, N$~with $a \geq 1$, where $\log a = \log t_{0} < \log t_{1} < \dots < \log t_{N}= \log T$ is a partition of $[\log a, \log T]$. 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.
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Green, C. W. H., & Yan, Y. (2022). Detailed error analysis for a fractional Adams method on caputo–hadamard fractional differential equations. Foundations, 2(4), 839-861. https://doi.org/10.3390/foundations2040057
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MDPI
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Foundations
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2673-9321