Fixed point approach to the Mittag-Leffler kernel-related fractional differential equations

AIMS Mathematics

article

Hasanen A. Hammad¹  Hüseyin Işık³  Hassen Aydi⁴  Manuel De la Sen⁷ 

[1] Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University;Department of Mathematics, Faculty of Science, Sohag University;Department of Engineering Science, Bandırma Onyedi Eylül University;Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse;China Medical University Hospital, China Medical University;Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University;Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country

关键词: fractional differential equation;    Atangana-Baleanu fractional operator;    fixed point methodology;    Riemann-Liouville fractional integral;   

DOI  :  10.3934/math.2023433

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The goal of this paper is to present a new class of contraction mappings, so-called $ \eta _{\theta }^{\ell } $-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for $ \eta _{\theta }^{\ell } $-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.

【 授权许可】

CC BY