Numerical methods for Caputo-Hadamard fractional differential equations with graded and non-uniform meshes
dc.contributor.author | Green, Charles | |
dc.contributor.author | Liu, Yanzhi | |
dc.contributor.author | Yan, Yubin | |
dc.date.accessioned | 2022-05-20T12:16:54Z | |
dc.date.available | 2022-05-20T12:16:54Z | |
dc.identifier | https://chesterrep.openrepository.com/bitstream/handle/10034/626879/greliuyan.pdf?sequence=1 | |
dc.identifier.citation | Green, C. W. H., Liu, Y., & Yan, Y. (2021). Numerical Methods for Caputo–Hadamard Fractional Differential Equations with Graded and Non-Uniform Meshes. Mathematics, 9(21), 2728. https://doi.org/10.3390/math9212728 | en_US |
dc.identifier.uri | http://hdl.handle.net/10034/626879 | |
dc.description.abstract | We consider the predictor-corrector numerical methods for solving Caputo-Hadamard fractional differential equation with the graded meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \big ( \frac{j}{N} \big )^{r}, \, j=0, 1, 2, \dots, N$ with $a \geq 1$ and $ r \geq 1$, where $\log a = \log t_{0} < \log t_{1} < \dots < \log t_{N}= \log T$ is a partition of $[\log t_{0}, \log T]$. We also consider the rectangular and trapezoidal methods for solving Caputo-Hadamard fractional differential equation with the non-uniform meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \frac{j (j+1)}{N(N+1)}, \, j=0, 1, 2, \dots, N$. Under the weak smoothness assumptions of the Caputo-Hadamard fractional derivative, e.g., $\prescript{}{CH}D^\alpha_{a,t}y(t) \notin C^{1}[a, T]$ with $ \alpha \in (0, 2)$, the optimal convergence orders of the proposed numerical methods are obtained by choosing the suitable graded mesh ratio $r \geq 1$. The numerical examples are given to show that the numerical results are consistent with the theoretical findings. | en_US |
dc.publisher | MDPI | en_US |
dc.relation.url | https://www.mdpi.com/2227-7390/9/21/2728 | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_US |
dc.subject | Caputo fractional derivative | en_US |
dc.subject | Hadamard caputo fractional derivative | en_US |
dc.subject | graded meshes | en_US |
dc.subject | error estimates | en_US |
dc.title | Numerical methods for Caputo-Hadamard fractional differential equations with graded and non-uniform meshes | en_US |
dc.type | Article | en_US |
dc.identifier.eissn | 2227-7390 | en_US |
dc.contributor.department | University of Chester; Lvliang University | en_US |
dc.identifier.journal | Mathematics | en_US |
or.grant.openaccess | Yes | en_US |
rioxxterms.funder | unfunded | en_US |
rioxxterms.identifier.project | unfunded | en_US |
rioxxterms.version | AM | en_US |
rioxxterms.versionofrecord | 10.3390/math9212728 | en_US |
rioxxterms.licenseref.startdate | 2022-05-20 | |
dcterms.dateAccepted | 2021-10-25 | |
rioxxterms.publicationdate | 2021-10-27 | |
dc.date.deposited | 20/5/22 | en_US |
dc.indentifier.issn | 2227-7390 | en_US |