A New Contraction in <i>b</i>-Metric-Like Spaces with an Application

In this paper, via the concept of w-distance in b-metric-like space, we introduce a new contraction, called β-ζ-contraction. Furthermore, we get the existence and uniqueness of the corresponding fixed point. In addition, we also furnish several examples to demonstrate the validity and practical applicability of our findings. Finally, we utilize the derived outcomes to address problems within differential equations.