Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative
Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction...
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SpringerOpen
2021-07-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-021-03476-9 |
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doaj-4144fa8d0f2448c2ab6fc7c575058cc52021-07-04T11:11:18ZengSpringerOpenAdvances in Difference Equations1687-18472021-07-012021111310.1186/s13662-021-03476-9Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivativeHojjat Afshari0Hossein Hosseinpour1H. R. Marasi2Department of Mathematics, Faculty of Basic Sciences, University of BonabDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of TabrizDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of TabrizAbstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete F $\mathfrak{F}$ -metric spaces for this purpose.https://doi.org/10.1186/s13662-021-03476-9Caputo–Fabrizio fractional derivativeF $\mathfrak{F}$ -metric spaceα-ℓ-contraction mappingFixed point |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hojjat Afshari Hossein Hosseinpour H. R. Marasi |
| spellingShingle |
Hojjat Afshari Hossein Hosseinpour H. R. Marasi Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative Advances in Difference Equations Caputo–Fabrizio fractional derivative F $\mathfrak{F}$ -metric space α-ℓ-contraction mapping Fixed point |
| author_facet |
Hojjat Afshari Hossein Hosseinpour H. R. Marasi |
| author_sort |
Hojjat Afshari |
| title |
Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative |
| title_short |
Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative |
| title_full |
Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative |
| title_fullStr |
Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative |
| title_full_unstemmed |
Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative |
| title_sort |
application of some new contractions for existence and uniqueness of differential equations involving caputo–fabrizio derivative |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2021-07-01 |
| description |
Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First we apply α-ℓ-contraction and α-type F-contraction mappings to study the existence and uniqueness of solutions for such problems. Finally, we use some contraction mappings in complete F $\mathfrak{F}$ -metric spaces for this purpose. |
| topic |
Caputo–Fabrizio fractional derivative F $\mathfrak{F}$ -metric space α-ℓ-contraction mapping Fixed point |
| url |
https://doi.org/10.1186/s13662-021-03476-9 |
| work_keys_str_mv |
AT hojjatafshari applicationofsomenewcontractionsforexistenceanduniquenessofdifferentialequationsinvolvingcaputofabrizioderivative AT hosseinhosseinpour applicationofsomenewcontractionsforexistenceanduniquenessofdifferentialequationsinvolvingcaputofabrizioderivative AT hrmarasi applicationofsomenewcontractionsforexistenceanduniquenessofdifferentialequationsinvolvingcaputofabrizioderivative |
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1721320504599511040 |