Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

Monica-Felicia Bota; Liliana Guran; Monica-Felicia Bota; Liliana Guran

doi:10.3934/math.2022033

AIMS Mathematics

2022, Volume 7, Issue 1: 518-535. doi: 10.3934/math.2022033

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Research article

Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

Monica-Felicia Bota ^{1
,
,},
Liliana Guran ²

1.
Department of Mathematics, Babeș-Bolyai University, Kogǎlniceanu Street No. 1, 400084, Cluj-Napoca, Romania
2.
Department of Pharmaceutical Sciences, "Vasile Goldiș" Western University of Arad, L. Rebreanu Street, No. 86, 310048, Arad, Romania

Received: 11 May 2021 Accepted: 22 September 2021 Published: 13 October 2021
MSC : 46T99, 47H10, 54H25

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.
- fixed point,
- extended $ b $-metric space,
- $ \varphi $-contraction,
- $ \alpha $-$ \varphi $-contraction,
- well-posedness,
- integral equations,
- fractional differential equations
Citation: Monica-Felicia Bota, Liliana Guran. Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces[J]. AIMS Mathematics, 2022, 7(1): 518-535. doi: 10.3934/math.2022033

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Abstract

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.

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