Application of some new contractions for existence and uniqueness of differential equations involving Caputo–Fabrizio derivative

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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Bibliographic Details
Main Authors: Hojjat Afshari, Hossein Hosseinpour, H. R. Marasi
Format: Article
Language:English
Published: SpringerOpen 2021-07-01
Series:Advances in Difference Equations
Subjects:
Caputo–Fabrizio fractional derivative
F $\mathfrak{F}$ -metric space
α-ℓ-contraction mapping
Fixed point
Online Access:https://doi.org/10.1186/s13662-021-03476-9
Description
Summary: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.
ISSN:1687-1847

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