An Implicit Relation Approach in Metric Spaces under w -Distance and Application to Fractional Differential Equation

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.