Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense
This study will introduce a new differentiation operator, the Hilfer fractional-fractal derivative (H-FFD). The new proposed derivative aims to attract more non-local problems that show with the same time fractal behaviors. For numerical settlement of initial value problems, we use the shifted Legen...
| Main Authors: | , , , , |
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| Format: | Article |
| Published: |
Elesvier
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/103254/ |
| _version_ | 1848863971622256640 |
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| author | Shloof, A. M. Senu, N. Ahmadian, A. Nik Long, N. M. A. Salahshour, S. |
| author_facet | Shloof, A. M. Senu, N. Ahmadian, A. Nik Long, N. M. A. Salahshour, S. |
| author_sort | Shloof, A. M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This study will introduce a new differentiation operator, the Hilfer fractional-fractal derivative (H-FFD). The new proposed derivative aims to attract more non-local problems that show with the same time fractal behaviors. For numerical settlement of initial value problems, we use the shifted Legendre operational matrix. The main advantage of this method is that it reduces both linear and non-linear problems alike in solving the problem into a system of linear and non-linear algebraic equations. In addition, the numerical approximation of this new operator also offers some applications to systems of linear and non-linear problems. |
| first_indexed | 2025-11-15T13:41:24Z |
| format | Article |
| id | upm-103254 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:41:24Z |
| publishDate | 2022 |
| publisher | Elesvier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1032542023-11-21T07:32:28Z http://psasir.upm.edu.my/id/eprint/103254/ Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense Shloof, A. M. Senu, N. Ahmadian, A. Nik Long, N. M. A. Salahshour, S. This study will introduce a new differentiation operator, the Hilfer fractional-fractal derivative (H-FFD). The new proposed derivative aims to attract more non-local problems that show with the same time fractal behaviors. For numerical settlement of initial value problems, we use the shifted Legendre operational matrix. The main advantage of this method is that it reduces both linear and non-linear problems alike in solving the problem into a system of linear and non-linear algebraic equations. In addition, the numerical approximation of this new operator also offers some applications to systems of linear and non-linear problems. Elesvier 2022 Article PeerReviewed Shloof, A. M. and Senu, N. and Ahmadian, A. and Nik Long, N. M. A. and Salahshour, S. (2022) Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense. Applied Numerical Mathematics, 178. pp. 386-403. ISSN 0168-9274 https://www.sciencedirect.com/science/article/pii/S0168927422000393 10.1016/j.apnum.2022.02.006 |
| spellingShingle | Shloof, A. M. Senu, N. Ahmadian, A. Nik Long, N. M. A. Salahshour, S. Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title | Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title_full | Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title_fullStr | Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title_full_unstemmed | Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title_short | Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense |
| title_sort | solving fractal-fractional differential equations using operational matrix of derivatives via hilfer fractal-fractional derivative sense |
| url | http://psasir.upm.edu.my/id/eprint/103254/ http://psasir.upm.edu.my/id/eprint/103254/ http://psasir.upm.edu.my/id/eprint/103254/ |