One-sided Frobenius pairs in extriangulated categories

Let $\mathscr{C}$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. We introduce the notions left Frobenius pairs, ($n$-)cotorsion pairs and (weak) Auslander-Buchweitz contexts respect to in $\mathscr{C}$. show how construct cotorsion pais from $n$-cotorsion establish one-to-one correspondence between contexts. also study relation certain that pairs. These work generalize Ma-Zhao-Huang's results triangulated categories partially Becerril-Mendoza-P\'{e}rez-Santiago's abelian categories.