The goal of this paper is to present a new class of contraction mappings, so-called (Equation presented)-contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for (Equation presented)-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.
- Atangana-Baleanu fractional operator
- Riemann-Liouville fractional integral
- fixed point methodology
- fractional differential equation