Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations
In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order α∈ (0 , 1 ). The accuracy of these two methods is shown to be of order (3 - α) which improves some previous work done to date. To demonstrate the accuracy and usefulnes...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/173204 |
| _version_ | 1811694468588371968 |
|---|---|
| author | Li, Xuhao Wong, Patricia Jia Yiing |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Li, Xuhao Wong, Patricia Jia Yiing |
| author_sort | Li, Xuhao |
| collection | NTU |
| description | In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order α∈ (0 , 1 ). The accuracy of these two methods is shown to be of order (3 - α) which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations. |
| first_indexed | 2024-10-01T07:08:03Z |
| format | Journal Article |
| id | ntu-10356/173204 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:08:03Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1732042024-01-17T04:43:07Z Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations Li, Xuhao Wong, Patricia Jia Yiing School of Electrical and Electronic Engineering Science::Mathematics Generalized Fractional Derivative Caputo Fractional Derivative In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order α∈ (0 , 1 ). The accuracy of these two methods is shown to be of order (3 - α) which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations. The research of Xuhao Li was supported by Anhui Provincial Natural Science Foundation (Grant No. 2208085QA02). 2024-01-17T04:43:07Z 2024-01-17T04:43:07Z 2023 Journal Article Li, X. & Wong, P. J. Y. (2023). Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations. Journal of Applied Mathematics and Computing, 69(6), 4689-4716. https://dx.doi.org/10.1007/s12190-023-01944-x 1598-5865 https://hdl.handle.net/10356/173204 10.1007/s12190-023-01944-x 2-s2.0-85178176145 6 69 4689 4716 en Journal of Applied Mathematics and Computing © 2023 The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics. All rights reserved. |
| spellingShingle | Science::Mathematics Generalized Fractional Derivative Caputo Fractional Derivative Li, Xuhao Wong, Patricia Jia Yiing Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title_full | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title_fullStr | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title_full_unstemmed | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title_short | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
| title_sort | two new approximations for generalized caputo fractional derivative and their application in solving generalized fractional sub diffusion equations |
| topic | Science::Mathematics Generalized Fractional Derivative Caputo Fractional Derivative |
| url | https://hdl.handle.net/10356/173204 |
| work_keys_str_mv | AT lixuhao twonewapproximationsforgeneralizedcaputofractionalderivativeandtheirapplicationinsolvinggeneralizedfractionalsubdiffusionequations AT wongpatriciajiayiing twonewapproximationsforgeneralizedcaputofractionalderivativeandtheirapplicationinsolvinggeneralizedfractionalsubdiffusionequations |