Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix
This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems b...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nigerian Society of Physical Sciences
2023
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| Online Access: | http://psasir.upm.edu.my/id/eprint/108813/1/Solving%20fractional%20variable-order%20differential%20equations.pdf |
| _version_ | 1825939663677816832 |
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| author | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. |
| author_facet | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. |
| author_sort | Basim, M. |
| collection | UPM |
| description | This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems by reducing them to ones that can be solved by solving a set of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The suggested approaches are applied in solving non-linear and linear ABC problems according to initial conditions, and the efficiency and applicability of the proposed method are proved by several test examples. A lot of focus is placed on contrasting the numerical outcomes discovered by the new algorithm together with those discovered by previously well-known methods. |
| first_indexed | 2024-12-09T02:20:48Z |
| format | Article |
| id | upm.eprints-108813 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-12-09T02:20:48Z |
| publishDate | 2023 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | dspace |
| spelling | upm.eprints-1088132024-10-11T08:34:13Z http://psasir.upm.edu.my/id/eprint/108813/ Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems by reducing them to ones that can be solved by solving a set of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The suggested approaches are applied in solving non-linear and linear ABC problems according to initial conditions, and the efficiency and applicability of the proposed method are proved by several test examples. A lot of focus is placed on contrasting the numerical outcomes discovered by the new algorithm together with those discovered by previously well-known methods. Nigerian Society of Physical Sciences 2023-05-05 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/108813/1/Solving%20fractional%20variable-order%20differential%20equations.pdf Basim, M. and Senu, N. and Ahmadian, A. and Ibrahim, Z. B. and Salahshour, S. (2023) Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix. Journal of the Nigerian Society of Physical Sciences, 5 (2). art. no. 1221. pp. 1-11. ISSN 2714-4704; ESSN: 2714-2817 https://journal.nsps.org.ng/index.php/jnsps/article/view/1221 10.46481/jnsps.2023.1221 |
| spellingShingle | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title | Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title_full | Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title_fullStr | Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title_full_unstemmed | Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title_short | Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix |
| title_sort | solving fractional variable order differential equations of the non singular derivative using jacobi operational matrix |
| url | http://psasir.upm.edu.my/id/eprint/108813/1/Solving%20fractional%20variable-order%20differential%20equations.pdf |
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