Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation
In this study, we focus on demonstrating the stability of the three-step Z-iterative scheme within the context of weak contraction mappings as defined by Berinde. Further, we attain results concerning stability, data dependence, and error accumulation of the Z-iterative scheme. This article also in...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-07-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://journals.vu.lt./nonlinear-analysis/article/view/35403 |
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| author | Salman Zaheer Ankush Chanda Hemant Kumar Nashine |
| author_facet | Salman Zaheer Ankush Chanda Hemant Kumar Nashine |
| author_sort | Salman Zaheer |
| collection | DOAJ |
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In this study, we focus on demonstrating the stability of the three-step Z-iterative scheme within the context of weak contraction mappings as defined by Berinde. Further, we attain results concerning stability, data dependence, and error accumulation of the Z-iterative scheme. This article also includes a comparison of the convergence rates among various established iterative strategies. Several illustrative numerical examples are furnished to validate the accuracy and reliability of our findings. In the same spirit, we present an application that utilises the Z-iterative technique on Banach spaces to attain the solution of a delay Caputo fractional differential equation, building upon our primary findings.
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| format | Article |
| id | doaj-art-d8e867a6cebd43c6a09a6b58c74a23b0 |
| institution | Matheson Library |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-d8e867a6cebd43c6a09a6b58c74a23b02025-06-24T18:14:23ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-07-0129510.15388/namc.2024.29.35403Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equationSalman Zaheer0Ankush Chanda1Hemant Kumar Nashine2Vellore Institute of TechnologyVellore Institute of TechnologyUniversity of Johannesburg In this study, we focus on demonstrating the stability of the three-step Z-iterative scheme within the context of weak contraction mappings as defined by Berinde. Further, we attain results concerning stability, data dependence, and error accumulation of the Z-iterative scheme. This article also includes a comparison of the convergence rates among various established iterative strategies. Several illustrative numerical examples are furnished to validate the accuracy and reliability of our findings. In the same spirit, we present an application that utilises the Z-iterative technique on Banach spaces to attain the solution of a delay Caputo fractional differential equation, building upon our primary findings. https://journals.vu.lt./nonlinear-analysis/article/view/35403weak contractionsstabilitydata dependencyerror estimation, delay fractional differential equations |
| spellingShingle | Salman Zaheer Ankush Chanda Hemant Kumar Nashine Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation Nonlinear Analysis weak contractions stability data dependency error estimation, delay fractional differential equations |
| title | Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation |
| title_full | Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation |
| title_fullStr | Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation |
| title_full_unstemmed | Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation |
| title_short | Reckoning applications of Z-iteration: Data dependence and solution to a delay Caputo fractional differential equation |
| title_sort | reckoning applications of z iteration data dependence and solution to a delay caputo fractional differential equation |
| topic | weak contractions stability data dependency error estimation, delay fractional differential equations |
| url | https://journals.vu.lt./nonlinear-analysis/article/view/35403 |
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