An implicit relation approach in metric spaces under \(w\)-distance and application to fractional differential equation (Q2050375)

Summary: The purpose of this work is to introduce a new class of implicit relation and implicit type contractive condition in metric spaces under \(w\)-distance functional. Further, we derive fixed point results under a new class of contractive condition followed by three suitable examples. Next, we discuss results about weak well-posed property, weak limit shadowing property, and generalized \(w\)-Ulam-Hyers stability of the mappings of a given type. Finally, we obtain sufficient conditions for the existence of solutions for fractional differential equations as an application of the main result.