On the source problem for the diffusion equations with conformable derivative
In this article, we are interested in the problem of finding the source function of the diffusions equations \(\partial_{t}^\alpha - \Delta u = f(x)\) (where \(f\) as the unknown source function and \(\alpha\in (0,1)\)). Furthermore, the fractional derivative \(\alpha\) of \(u\) is defined by the C...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Tuncer Acar
2024-04-01
|
| Series: | Modern Mathematical Methods |
| Subjects: | |
| Online Access: | https://modernmathmeth.com/index.php/pub/article/view/24 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849729941517631488 |
|---|---|
| author | Van Anh Nghiem Thi Anh Tuan Vu Dinh Long Le Vuong Nguyen Doan |
| author_facet | Van Anh Nghiem Thi Anh Tuan Vu Dinh Long Le Vuong Nguyen Doan |
| author_sort | Van Anh Nghiem Thi |
| collection | DOAJ |
| description | In this article, we are interested in the problem of finding the source function of the diffusions equations \(\partial_{t}^\alpha - \Delta u = f(x)\) (where \(f\) as the unknown source function and \(\alpha\in (0,1)\)). Furthermore, the fractional derivative \(\alpha\) of \(u\) is defined by the Conformable time derivative. This is an ill-posed problem. So, we use the Reguralized Tikhonov method to construct a regularization solution, and the estimation of convergence is also discussed. |
| format | Article |
| id | doaj-art-ff8d848b641f425f96a09974d339d299 |
| institution | DOAJ |
| issn | 3023-5294 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Tuncer Acar |
| record_format | Article |
| series | Modern Mathematical Methods |
| spelling | doaj-art-ff8d848b641f425f96a09974d339d2992025-08-20T03:09:02ZengTuncer AcarModern Mathematical Methods3023-52942024-04-0122556424On the source problem for the diffusion equations with conformable derivativeVan Anh Nghiem Thi0https://orcid.org/0000-0002-1211-6241Anh Tuan Vu1https://orcid.org/0009-0003-9938-6619Dinh Long Le2https://orcid.org/0000-0001-8805-4588Vuong Nguyen Doan3https://orcid.org/0000-0002-9438-6439Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, VietnamFaculty of Fundamental Sciences, Dong Nai Technology University, Bien Hoa City, VietnamFaculty of Math, FPT University HCM, Saigon Hi-Tech Park, Thu Duc City, Ho Chi Minh City, VietnamFaculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, VietnamIn this article, we are interested in the problem of finding the source function of the diffusions equations \(\partial_{t}^\alpha - \Delta u = f(x)\) (where \(f\) as the unknown source function and \(\alpha\in (0,1)\)). Furthermore, the fractional derivative \(\alpha\) of \(u\) is defined by the Conformable time derivative. This is an ill-posed problem. So, we use the Reguralized Tikhonov method to construct a regularization solution, and the estimation of convergence is also discussed.https://modernmathmeth.com/index.php/pub/article/view/24conformable derivativeill-posedsource functiondiffusion equations |
| spellingShingle | Van Anh Nghiem Thi Anh Tuan Vu Dinh Long Le Vuong Nguyen Doan On the source problem for the diffusion equations with conformable derivative Modern Mathematical Methods conformable derivative ill-posed source function diffusion equations |
| title | On the source problem for the diffusion equations with conformable derivative |
| title_full | On the source problem for the diffusion equations with conformable derivative |
| title_fullStr | On the source problem for the diffusion equations with conformable derivative |
| title_full_unstemmed | On the source problem for the diffusion equations with conformable derivative |
| title_short | On the source problem for the diffusion equations with conformable derivative |
| title_sort | on the source problem for the diffusion equations with conformable derivative |
| topic | conformable derivative ill-posed source function diffusion equations |
| url | https://modernmathmeth.com/index.php/pub/article/view/24 |
| work_keys_str_mv | AT vananhnghiemthi onthesourceproblemforthediffusionequationswithconformablederivative AT anhtuanvu onthesourceproblemforthediffusionequationswithconformablederivative AT dinhlongle onthesourceproblemforthediffusionequationswithconformablederivative AT vuongnguyendoan onthesourceproblemforthediffusionequationswithconformablederivative |