On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces
In this paper, we consider a faster iterative method for approximating the fixed points of generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/3/166 |
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| author | James Abah Ugboh Joseph Oboyi Mfon Okon Udo Hossam A. Nabwey Austine Efut Ofem Ojen Kumar Narain |
| author_facet | James Abah Ugboh Joseph Oboyi Mfon Okon Udo Hossam A. Nabwey Austine Efut Ofem Ojen Kumar Narain |
| author_sort | James Abah Ugboh |
| collection | DOAJ |
| description | In this paper, we consider a faster iterative method for approximating the fixed points of generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results. |
| first_indexed | 2024-04-24T18:16:16Z |
| format | Article |
| id | doaj.art-d0293c52bbcc497eae038d7174b54ed9 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-04-24T18:16:16Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d0293c52bbcc497eae038d7174b54ed92024-03-27T13:42:07ZengMDPI AGFractal and Fractional2504-31102024-03-018316610.3390/fractalfract8030166On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach SpacesJames Abah Ugboh0Joseph Oboyi1Mfon Okon Udo2Hossam A. Nabwey3Austine Efut Ofem4Ojen Kumar Narain5Department of Mathematics, University of Calabar, Calabar P.O. Box 1115, NigeriaDepartment of Mathematics, University of Calabar, Calabar P.O. Box 1115, NigeriaDepartment of Mathematics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin P.O. Box 1167, NigeriaDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South AfricaIn this paper, we consider a faster iterative method for approximating the fixed points of generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results.https://www.mdpi.com/2504-3110/8/3/166fixed pointiterative methodfractional delay differential equationstrong convergence |
| spellingShingle | James Abah Ugboh Joseph Oboyi Mfon Okon Udo Hossam A. Nabwey Austine Efut Ofem Ojen Kumar Narain On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces Fractal and Fractional fixed point iterative method fractional delay differential equation strong convergence |
| title | On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces |
| title_full | On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces |
| title_fullStr | On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces |
| title_full_unstemmed | On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces |
| title_short | On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces |
| title_sort | on a faster iterative method for solving fractional delay differential equations in banach spaces |
| topic | fixed point iterative method fractional delay differential equation strong convergence |
| url | https://www.mdpi.com/2504-3110/8/3/166 |
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