Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations
This paper proposes some iterative constructions of fixed points for showing the existence and uniqueness of solutions for functional equations and fractional differential equations (FDEs) in the framework of CAT (0) spaces. Our new approach is based on the M∗-iterative scheme and the class of mappi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/6677650 |
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| _version_ | 1832553059114287104 |
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| author | Latif Ur Rahman Muhammad Arshad Sabri T. M. Thabet Imed Kedim |
| author_facet | Latif Ur Rahman Muhammad Arshad Sabri T. M. Thabet Imed Kedim |
| author_sort | Latif Ur Rahman |
| collection | DOAJ |
| description | This paper proposes some iterative constructions of fixed points for showing the existence and uniqueness of solutions for functional equations and fractional differential equations (FDEs) in the framework of CAT (0) spaces. Our new approach is based on the M∗-iterative scheme and the class of mappings with the KSC condition. We first obtain some ∆ and strong convergence theorems using M∗-iterative scheme. Using one of our main results, we solve a FDE from a broad class of fractional calculus. Eventually, we support our main results with a numerical example. A comparative numerical experiment shows that the M∗-iterative scheme produces high accurate numerical results corresponding to the other schemes in the literature. Our results are new and generalize several comparable results in fixed point theory and applications. |
| format | Article |
| id | doaj-art-56e817cf14ae45d9b10795d35dbdefc3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-56e817cf14ae45d9b10795d35dbdefc32025-02-03T05:57:01ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/6677650Iterative Construction of Fixed Points for Functional Equations and Fractional Differential EquationsLatif Ur Rahman0Muhammad Arshad1Sabri T. M. Thabet2Imed Kedim3Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsThis paper proposes some iterative constructions of fixed points for showing the existence and uniqueness of solutions for functional equations and fractional differential equations (FDEs) in the framework of CAT (0) spaces. Our new approach is based on the M∗-iterative scheme and the class of mappings with the KSC condition. We first obtain some ∆ and strong convergence theorems using M∗-iterative scheme. Using one of our main results, we solve a FDE from a broad class of fractional calculus. Eventually, we support our main results with a numerical example. A comparative numerical experiment shows that the M∗-iterative scheme produces high accurate numerical results corresponding to the other schemes in the literature. Our results are new and generalize several comparable results in fixed point theory and applications.http://dx.doi.org/10.1155/2023/6677650 |
| spellingShingle | Latif Ur Rahman Muhammad Arshad Sabri T. M. Thabet Imed Kedim Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations Journal of Mathematics |
| title | Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations |
| title_full | Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations |
| title_fullStr | Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations |
| title_full_unstemmed | Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations |
| title_short | Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations |
| title_sort | iterative construction of fixed points for functional equations and fractional differential equations |
| url | http://dx.doi.org/10.1155/2023/6677650 |
| work_keys_str_mv | AT latifurrahman iterativeconstructionoffixedpointsforfunctionalequationsandfractionaldifferentialequations AT muhammadarshad iterativeconstructionoffixedpointsforfunctionalequationsandfractionaldifferentialequations AT sabritmthabet iterativeconstructionoffixedpointsforfunctionalequationsandfractionaldifferentialequations AT imedkedim iterativeconstructionoffixedpointsforfunctionalequationsandfractionaldifferentialequations |