Open AccessExistence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces
Author(s) -
Monica-Felicia Bota,
Liliana Guran
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022033
Subject(s) - mathematics , fixed point theorem , fixed point , type (biology) , metric space , mathematical analysis , nonlinear system , operator (biology) , fractional calculus , metric (unit) , pure mathematics , physics , ecology , biochemistry , chemistry , operations management , repressor , quantum mechanics , gene , transcription factor , economics , biology
The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.