On Extended Branciari b-Distance Spaces and Applications to Fractional Differential Equations. (15th May 2021) - Jain, Reena; Nashine, Hemant Kumar; George, Reny; Mitrović, Zoran D.
Abstract : 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.