In this paper we study superderivations and Jordan superderivations of incidence superalgebras of locally finite ${\mathbb{Z}}_2$-graded posets. We prove that every superderivation can be expressed as a sum of an inner superderivation, an additive superderivation, and a ring superderivation; if the coefficient ring has inner derivations only, then every superderivation is inner. We also show that every Jordan superderivation decomposes uniquely as a sum of a superderivation and a proper Jordan superderivation that vanishes on the even part. These results extend classical results on incidence algebras to the supersetting.

In this article, we establish the existence and uniqueness of coupled coincidence fixed points for rational-type contraction mappings in the framework of metric spaces by employing a binary relation. These results are derived under the assumption of the mixed monotone property. To illustrate the effectiveness of the obtained results, a suitable example is provided. Finally, we give an application of our main results to a fractional differential equation involving the Riemann–Liouville fractional derivatives. These findings extend existing results in the literature and highlight the effectiveness of the proposed approach in the analysis of fractional differential equations.