Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation
In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to...
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2022-04-01
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| Series: | Cubo |
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| Online Access: | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/2957 |
| _version_ | 1811292295834632192 |
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| author | Abderrahim Guerfi Abdelouaheb Ardjouni |
| author_facet | Abderrahim Guerfi Abdelouaheb Ardjouni |
| author_sort | Abderrahim Guerfi |
| collection | DOAJ |
| description | In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results. |
| first_indexed | 2024-04-13T04:43:18Z |
| format | Article |
| id | doaj.art-5d02685f25b84fc89dae4707a6062622 |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-04-13T04:43:18Z |
| publishDate | 2022-04-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-5d02685f25b84fc89dae4707a60626222022-12-22T03:01:56ZengUniversidad de La FronteraCubo0716-77760719-06462022-04-01241839410.4067/S0719-06462022000100083Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equationAbderrahim Guerfi0https://orcid.org/0000-0002-8221-9545Abdelouaheb Ardjouni1https://orcid.org/0000-0003-0216-1265Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria – Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.https://revistas.ufro.cl/ojs/index.php/cubo/article/view/2957iterative fractional differential equationsfixed point theoremexistenceuniquenesscontinuous dependenceulam stability |
| spellingShingle | Abderrahim Guerfi Abdelouaheb Ardjouni Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation Cubo iterative fractional differential equations fixed point theorem existence uniqueness continuous dependence ulam stability |
| title | Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation |
| title_full | Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation |
| title_fullStr | Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation |
| title_full_unstemmed | Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation |
| title_short | Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation |
| title_sort | existence uniqueness continuous dependence and ulam stability of mild solutions for an iterative fractional differential equation |
| topic | iterative fractional differential equations fixed point theorem existence uniqueness continuous dependence ulam stability |
| url | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/2957 |
| work_keys_str_mv | AT abderrahimguerfi existenceuniquenesscontinuousdependenceandulamstabilityofmildsolutionsforaniterativefractionaldifferentialequation AT abdelouahebardjouni existenceuniquenesscontinuousdependenceandulamstabilityofmildsolutionsforaniterativefractionaldifferentialequation |