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

[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.

[学科分类] 地球科学(综合)

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