Abstract
In this paper, we introduce the notion of generalized L-contractions which enlarge the class of Script capital L-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L*-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari's metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.