Citation
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
Abstract
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.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.3390/math9161987 |
| Publisher: | MDPI |
| Keywords: | Fractional derivatives; Caputo derivative; Fractional advection–diffusion equation; Finite difference schemes; Integral conditions |
| Depositing User: | Ms. Che Wa Zakaria |
| Date Deposited: | 14 Sep 2022 08:42 |
| Last Modified: | 14 Sep 2022 08:42 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/math9161987 |
| URI: | http://psasir.upm.edu.my/id/eprint/95549 |
| Statistic Details: | View Download Statistic |
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