On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations.
In this paper we define, for the first time, the modified fractional derivative with Mittage-Leffler kernel of Riemann-Liouville (R-L) type of arbitrary order [Formula: see text]delta. We derive the infinite series representations for the modified derivatives of R-L and Caputo types and present a re...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0325897 |
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| author | Mohammed Al-Refai Dumitru Baleanu A K Alomari |
| author_facet | Mohammed Al-Refai Dumitru Baleanu A K Alomari |
| author_sort | Mohammed Al-Refai |
| collection | DOAJ |
| description | In this paper we define, for the first time, the modified fractional derivative with Mittage-Leffler kernel of Riemann-Liouville (R-L) type of arbitrary order [Formula: see text]delta. We derive the infinite series representations for the modified derivatives of R-L and Caputo types and present a relationship between them. We also investigate the modified derivatives for the Dirac delta functions, and study related fractional differential equations. Explicit solutions were presented for linear fractional differential equations with constant coefficients via the Laplace transform. A fractional model with the modified derivative is considered and numerical simulations were presented. |
| format | Article |
| id | doaj-art-2b913f78aaa8468d80f7317a442fec02 |
| institution | OA Journals |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-2b913f78aaa8468d80f7317a442fec022025-08-20T02:36:53ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01206e032589710.1371/journal.pone.0325897On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations.Mohammed Al-RefaiDumitru BaleanuA K AlomariIn this paper we define, for the first time, the modified fractional derivative with Mittage-Leffler kernel of Riemann-Liouville (R-L) type of arbitrary order [Formula: see text]delta. We derive the infinite series representations for the modified derivatives of R-L and Caputo types and present a relationship between them. We also investigate the modified derivatives for the Dirac delta functions, and study related fractional differential equations. Explicit solutions were presented for linear fractional differential equations with constant coefficients via the Laplace transform. A fractional model with the modified derivative is considered and numerical simulations were presented.https://doi.org/10.1371/journal.pone.0325897 |
| spellingShingle | Mohammed Al-Refai Dumitru Baleanu A K Alomari On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. PLoS ONE |
| title | On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. |
| title_full | On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. |
| title_fullStr | On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. |
| title_full_unstemmed | On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. |
| title_short | On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations. |
| title_sort | on the solutions of fractional differential equations with modified mittag leffler kernel and dirac delta function analytical results and numerical simulations |
| url | https://doi.org/10.1371/journal.pone.0325897 |
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