Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations
The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which enta...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024280?viewType=HTML |
| _version_ | 1797301854597545984 |
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| author | Abdon Atangana Seda İğret Araz |
| author_facet | Abdon Atangana Seda İğret Araz |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge. |
| first_indexed | 2024-03-07T23:28:27Z |
| format | Article |
| id | doaj.art-3833bb0f298f445b88d9dfbc3d8eb452 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T23:28:27Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3833bb0f298f445b88d9dfbc3d8eb4522024-02-21T01:27:29ZengAIMS PressAIMS Mathematics2473-69882024-01-01935763579310.3934/math.2024280Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equationsAbdon Atangana0Seda İğret Araz 11. Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa 2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan 3. IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 70800 Ostrava-Poruba, Czech Republic1. Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa4. Faculty of Education, Siirt University, Siirt, TurkeyThe existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge.https://www.aimspress.com/article/doi/10.3934/math.2024280?viewType=HTMLfractal-fractional differentiation and integrationchaplygin's methodexistence and uniqueness |
| spellingShingle | Abdon Atangana Seda İğret Araz Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations AIMS Mathematics fractal-fractional differentiation and integration chaplygin's method existence and uniqueness |
| title | Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations |
| title_full | Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations |
| title_fullStr | Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations |
| title_full_unstemmed | Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations |
| title_short | Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations |
| title_sort | extension of chaplygin s existence and uniqueness method for fractal fractional nonlinear differential equations |
| topic | fractal-fractional differentiation and integration chaplygin's method existence and uniqueness |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024280?viewType=HTML |
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