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In this work, we define new  α − λ -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.

journal of function spaces

On Extended Branciari <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>b</mi> </math>-Distance Spaces and Applications to Fractional Differential Equations

On Extended Branciari b -Distance Spaces and Applications to Fractional Differential Equations

On Extended Branciari $b$ -Distance Spaces and Applications to Fractional Differential Equations