Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions
In this work, we investigate the existence, uniqueness, and different stability types, focusing on Ulam-Hyers stability, of a solution to a nonlinear fuzzy fractional differential equation with Caputo generalized Hukuhara differentiability of order ℘ ∈ (n − 1, n). We establish explicit criteria to g...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-07-01
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| Series: | Journal of Fuzzy Extension and Applications |
| Subjects: | |
| Online Access: | https://www.journal-fea.com/article_199563_e656f850bd0f0a522a58543dac9c47d1.pdf |
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| author | Brahim Ghrissi Abdelkader Amara Youcef Henka |
| author_facet | Brahim Ghrissi Abdelkader Amara Youcef Henka |
| author_sort | Brahim Ghrissi |
| collection | DOAJ |
| description | In this work, we investigate the existence, uniqueness, and different stability types, focusing on Ulam-Hyers stability, of a solution to a nonlinear fuzzy fractional differential equation with Caputo generalized Hukuhara differentiability of order ℘ ∈ (n − 1, n). We establish explicit criteria to guarantee both the existence and uniqueness of the solution, employing the Banach fixed point theorem. Additionally, we present two examples to enhance the illustration of our findings. |
| format | Article |
| id | doaj-art-111dd2d43b4f4090b4da3576e2dfac17 |
| institution | Kabale University |
| issn | 2783-1442 2717-3453 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | Journal of Fuzzy Extension and Applications |
| spelling | doaj-art-111dd2d43b4f4090b4da3576e2dfac172025-01-30T15:07:12ZengAyandegan Institute of Higher Education,Journal of Fuzzy Extension and Applications2783-14422717-34532024-07-015335336410.22105/jfea.2024.453123.1448199563Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutionsBrahim Ghrissi0Abdelkader Amara1Youcef Henka2Laboratory of Applied Mathematics, Ouargla University, Ouargla, Algeria.Laboratory of Applied Mathematics, Ouargla University, Ouargla, Algeria.Laboratoire de Mathematiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, Algerie.In this work, we investigate the existence, uniqueness, and different stability types, focusing on Ulam-Hyers stability, of a solution to a nonlinear fuzzy fractional differential equation with Caputo generalized Hukuhara differentiability of order ℘ ∈ (n − 1, n). We establish explicit criteria to guarantee both the existence and uniqueness of the solution, employing the Banach fixed point theorem. Additionally, we present two examples to enhance the illustration of our findings.https://www.journal-fea.com/article_199563_e656f850bd0f0a522a58543dac9c47d1.pdfcaputo generalized hukuhara differentiabilitystability analysisfuzzy fractional differential equation |
| spellingShingle | Brahim Ghrissi Abdelkader Amara Youcef Henka Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions Journal of Fuzzy Extension and Applications caputo generalized hukuhara differentiability stability analysis fuzzy fractional differential equation |
| title | Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions |
| title_full | Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions |
| title_fullStr | Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions |
| title_full_unstemmed | Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions |
| title_short | Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions |
| title_sort | higher order fuzzy fractional differential equations on the existence uniqueness and hyers ulam rassias stability of solutions |
| topic | caputo generalized hukuhara differentiability stability analysis fuzzy fractional differential equation |
| url | https://www.journal-fea.com/article_199563_e656f850bd0f0a522a58543dac9c47d1.pdf |
| work_keys_str_mv | AT brahimghrissi higherorderfuzzyfractionaldifferentialequationsontheexistenceuniquenessandhyersulamrassiasstabilityofsolutions AT abdelkaderamara higherorderfuzzyfractionaldifferentialequationsontheexistenceuniquenessandhyersulamrassiasstabilityofsolutions AT youcefhenka higherorderfuzzyfractionaldifferentialequationsontheexistenceuniquenessandhyersulamrassiasstabilityofsolutions |