Theoretical and numerical aspect of fractional differential equations with purely integral conditions
In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫10v(x,t)dx and ∫10xnv(x,t)dx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequa...
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| Format: | Article |
| Language: | English |
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MDPI
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/95549/ http://psasir.upm.edu.my/id/eprint/95549/1/Theoretical%20and%20Numerical%20Aspect.pdf |
| _version_ | 1848862186594631680 |
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| author | Brahimi, Saadoune Merad, Ahcene Kilicman, Adem |
| author_facet | Brahimi, Saadoune Merad, Ahcene Kilicman, Adem |
| author_sort | Brahimi, Saadoune |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫10v(x,t)dx and ∫10xnv(x,t)dx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequalities known as the “a priori estimate” method relying on the range density of the operator generated by the considered problem. The approximate solution for this problem with these new kinds of boundary conditions is established by using a combination of the finite difference method and the numerical integration. Finally, we give some numerical tests to illustrate the usefulness of the obtained results. |
| first_indexed | 2025-11-15T13:13:01Z |
| format | Article |
| id | upm-95549 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T13:13:01Z |
| publishDate | 2021 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-955492022-09-14T08:42:55Z http://psasir.upm.edu.my/id/eprint/95549/ Theoretical and numerical aspect of fractional differential equations with purely integral conditions Brahimi, Saadoune Merad, Ahcene Kilicman, Adem In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫10v(x,t)dx and ∫10xnv(x,t)dx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequalities known as the “a priori estimate” method relying on the range density of the operator generated by the considered problem. The approximate solution for this problem with these new kinds of boundary conditions is established by using a combination of the finite difference method and the numerical integration. Finally, we give some numerical tests to illustrate the usefulness of the obtained results. MDPI 2021-08-19 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/95549/1/Theoretical%20and%20Numerical%20Aspect.pdf Brahimi, Saadoune and Merad, Ahcene and Kilicman, Adem (2021) Theoretical and numerical aspect of fractional differential equations with purely integral conditions. Mathematics, 9 (16). pp. 1-26. ISSN 2227-7390 https://www.mdpi.com/2227-7390/9/16/1987/htm 10.3390/math9161987 |
| spellingShingle | Brahimi, Saadoune Merad, Ahcene Kilicman, Adem Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title | Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title_full | Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title_fullStr | Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title_full_unstemmed | Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title_short | Theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| title_sort | theoretical and numerical aspect of fractional differential equations with purely integral conditions |
| url | http://psasir.upm.edu.my/id/eprint/95549/ http://psasir.upm.edu.my/id/eprint/95549/ http://psasir.upm.edu.my/id/eprint/95549/ http://psasir.upm.edu.my/id/eprint/95549/1/Theoretical%20and%20Numerical%20Aspect.pdf |