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| Titre: | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| Auteur(s): | Bourchi, Soumia
Jarad, Fahd
Adjabi, Yassine
Thabet, Abdeljawad
Mahariq, Ibrahim |
| Mots-clés: | Abstract Cauchy problem
Caputo type generalized fractional operators
Continuous dependence on parameters
Existence
Fixed point theorems
Mittag-Leffler type function
Stability
Uniformly continuous semigroups
Uniqueness |
| Date de publication: | 2023 |
| Editeur: | DergiPark |
| Collection/Numéro: | Advances in the Theory of Nonlinear Analysis and its Applications/ Vol.7, N°1(2023);pp. 1-28 |
| Résumé: | In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results |
| URI/URL: | https://doi.org/10.31197/atnaa.1147950
https://dergipark.org.tr/en/pub/atnaa/issue/73409/1147950
http://dlibrary.univ-boumerdes.dz:8080/handle/123456789/11144 |
| ISSN: | 25872648 |
| Collection(s) : | Publications Internationales
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