Conformable finite element method for conformable fractional partial differential equations
The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231479?viewType=HTML |
| _version_ | 1827769101582336000 |
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| author | Lakhlifa Sadek Tania A Lazǎr Ishak Hashim |
| author_facet | Lakhlifa Sadek Tania A Lazǎr Ishak Hashim |
| author_sort | Lakhlifa Sadek |
| collection | DOAJ |
| description | The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives. |
| first_indexed | 2024-03-11T12:19:31Z |
| format | Article |
| id | doaj.art-359050837e884ed788184a80b846578d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:19:31Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-359050837e884ed788184a80b846578d2023-11-07T01:40:14ZengAIMS PressAIMS Mathematics2473-69882023-10-01812288582887710.3934/math.20231479Conformable finite element method for conformable fractional partial differential equationsLakhlifa Sadek0Tania A Lazǎr 1Ishak Hashim21. Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tétouan, Morocco2. Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj Napoca, Romania3. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), Bangi 43650, Selangor, Malaysia 4. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab EmiratesThe finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.https://www.aimspress.com/article/doi/10.3934/math.20231479?viewType=HTMLccf-pdegalerkin methodconformable finite element (cfe) method |
| spellingShingle | Lakhlifa Sadek Tania A Lazǎr Ishak Hashim Conformable finite element method for conformable fractional partial differential equations AIMS Mathematics ccf-pde galerkin method conformable finite element (cfe) method |
| title | Conformable finite element method for conformable fractional partial differential equations |
| title_full | Conformable finite element method for conformable fractional partial differential equations |
| title_fullStr | Conformable finite element method for conformable fractional partial differential equations |
| title_full_unstemmed | Conformable finite element method for conformable fractional partial differential equations |
| title_short | Conformable finite element method for conformable fractional partial differential equations |
| title_sort | conformable finite element method for conformable fractional partial differential equations |
| topic | ccf-pde galerkin method conformable finite element (cfe) method |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231479?viewType=HTML |
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