On Solutions to Fractional Iterative Differential Equations with Caputo Derivative
In this paper, we are concerned with two points. First, the existence and uniqueness of the iterative fractional differential equation cDαcxt=ft,xt,xgxt are presented using the fixed-point theorem by imposing some conditions on f and g. Second, we proposed the iterative scheme that converges to the...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5598990 |
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| _version_ | 1832546593950138368 |
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| author | Alemnew Abera Benyam Mebrate |
| author_facet | Alemnew Abera Benyam Mebrate |
| author_sort | Alemnew Abera |
| collection | DOAJ |
| description | In this paper, we are concerned with two points. First, the existence and uniqueness of the iterative fractional differential equation cDαcxt=ft,xt,xgxt are presented using the fixed-point theorem by imposing some conditions on f and g. Second, we proposed the iterative scheme that converges to the fixed point. The convergence of the iterative scheme is proved, and different iterative schemes are compared with the proposed iterative scheme. We prepared algorithms to implement the proposed iterative scheme. We have successfully applied the proposed iterative scheme to the given iterative differential equations by taking examples for different values of α. |
| format | Article |
| id | doaj-art-4141a813228d421186b984752605a9ae |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4141a813228d421186b984752605a9ae2025-02-03T06:47:40ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/5598990On Solutions to Fractional Iterative Differential Equations with Caputo DerivativeAlemnew Abera0Benyam Mebrate1Department of MathematicsDepartment of MathematicsIn this paper, we are concerned with two points. First, the existence and uniqueness of the iterative fractional differential equation cDαcxt=ft,xt,xgxt are presented using the fixed-point theorem by imposing some conditions on f and g. Second, we proposed the iterative scheme that converges to the fixed point. The convergence of the iterative scheme is proved, and different iterative schemes are compared with the proposed iterative scheme. We prepared algorithms to implement the proposed iterative scheme. We have successfully applied the proposed iterative scheme to the given iterative differential equations by taking examples for different values of α.http://dx.doi.org/10.1155/2023/5598990 |
| spellingShingle | Alemnew Abera Benyam Mebrate On Solutions to Fractional Iterative Differential Equations with Caputo Derivative Journal of Mathematics |
| title | On Solutions to Fractional Iterative Differential Equations with Caputo Derivative |
| title_full | On Solutions to Fractional Iterative Differential Equations with Caputo Derivative |
| title_fullStr | On Solutions to Fractional Iterative Differential Equations with Caputo Derivative |
| title_full_unstemmed | On Solutions to Fractional Iterative Differential Equations with Caputo Derivative |
| title_short | On Solutions to Fractional Iterative Differential Equations with Caputo Derivative |
| title_sort | on solutions to fractional iterative differential equations with caputo derivative |
| url | http://dx.doi.org/10.1155/2023/5598990 |
| work_keys_str_mv | AT alemnewabera onsolutionstofractionaliterativedifferentialequationswithcaputoderivative AT benyammebrate onsolutionstofractionaliterativedifferentialequationswithcaputoderivative |