  Extriangulated categories were introduced by Nakaoka and Palu as a
simultaneous generalization of exact categories and triangulated categories. In
this paper, we first introduce the concept of left Frobenius pairs on an
extriangulated category C, and then establish a bijective correspondence
between Frobenius pairs and certain cotorsion pairs in C. As an application,
some new admissible model structures are established from left Frobenius pairs
under certain conditions, which generalizes a result of Hu et al. (J. Algebra
551 (2020) 23-60).
