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Research Article | Open Access

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

Monica-Felicia Bota1( ), Liliana Guran2
Department of Mathematics, Babeș-Bolyai University, Kogǎlniceanu Street No. 1, 400084, Cluj-Napoca, Romania
Department of Pharmaceutical Sciences, "Vasile Goldiș" Western University of Arad, L. Rebreanu Street, No. 86, 310048, Arad, Romania
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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 φ-contractions and α- φ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.

Keywords

fixed pointextended b-metric spaceφ-contractionα-φ-contractionwell-posednessintegral equationsfractional differential equations
CLC number: 46T99, 47H10, 54H25

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 518-535
DOI: 10.3934/math.2022033

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Bota M-F, Guran L. Existence of a solution of fractional differential equations using the fixed point technique in extended b-metric spaces. AIMS Mathematics, 2022, 7(1): 518-535. https://doi.org/10.3934/math.2022033

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Received: 11 May 2021
Accepted: 22 September 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)