Solving one type nonlinear differential equation using fuzzy W-contractions

Abstract

In this paper, we present a new type of contraction called $W$-contraction in fuzzy metric space. Utilizing  this contraction, we establish a unique fixed point theorem for self-map in the structure of fuzzy metric space which turns out to be generalization of fuzzy contraction given by Gregori et al. [8]. As an application of our result, we study the  existence and uniqueness of the solution to nonlinear ordinary differential equations. The article also includes an example which shows the validity of our results.