Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives
This article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. The original problem was converted into an equivalent...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241690 |
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| author | Debao Yan |
| author_facet | Debao Yan |
| author_sort | Debao Yan |
| collection | DOAJ |
| description | This article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. The original problem was converted into an equivalent integral equation. Banach's fixed-point principle and Shaefer's fixed-point theorem were exploited to ensure that two existence conditions of the solutions for the problems were established. In addition, the stability known as $ \beta $-Ulam-Hyers for such problems has also been analyzed. Illustrative examples demonstrated practical applications of the work. |
| format | Article |
| id | doaj-art-665b246914634dc39d4db9b515d3f97b |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-665b246914634dc39d4db9b515d3f97b2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912356263564410.3934/math.20241690Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivativesDebao Yan0School of Mathematics and Statistics, Heze University, Heze City, Shandong Province, 274000, ChinaThis article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. The original problem was converted into an equivalent integral equation. Banach's fixed-point principle and Shaefer's fixed-point theorem were exploited to ensure that two existence conditions of the solutions for the problems were established. In addition, the stability known as $ \beta $-Ulam-Hyers for such problems has also been analyzed. Illustrative examples demonstrated practical applications of the work.https://www.aimspress.com/article/doi/10.3934/math.20241690quantitative analysissequential fractional differential equationsvariable coefficients$ \beta $-ulam-hyers stability |
| spellingShingle | Debao Yan Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives AIMS Mathematics quantitative analysis sequential fractional differential equations variable coefficients $ \beta $-ulam-hyers stability |
| title | Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| title_full | Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| title_fullStr | Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| title_full_unstemmed | Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| title_short | Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| title_sort | quantitative analysis and stability results in beta normed space for sequential differential equations with variable coefficients involving two fractional derivatives |
| topic | quantitative analysis sequential fractional differential equations variable coefficients $ \beta $-ulam-hyers stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241690 |
| work_keys_str_mv | AT debaoyan quantitativeanalysisandstabilityresultsinbetanormedspaceforsequentialdifferentialequationswithvariablecoefficientsinvolvingtwofractionalderivatives |