Abstract
In this work, we define new alpha-lambda-rational contractive conditions and establish fixed-points results based on aforesaid contractive conditions for a mapping in extended Branciari b-distance spaces. We furnish two examples to justify the work. Further, we discuss results on weak well-posed property, weak limit shadowing property, and generalized w-Ulam-Hyers stability in the underlying space. Finally, as an application of our main result, we obtain sufficient conditions for the existence of solutions of a nonlinear fractional differential equation with integral boundary conditions.