New Relation-Theoretic Fixed Point Theorems in Fuzzy Metric Spaces with an Application to Fractional Differential Equations

Abstract

In this paper, we introduce the notion of fuzzy R−ψ−contractive mappings and prove some relevant results on the existence and uniqueness of fixed points for this type of mappings in the setting of non-Archimedean fuzzy metric spaces. Several illustrative examples are also given to support our newly proven results. Furthermore, we apply our main results to prove the existence and uniqueness of a solution for Caputo fractional differential equations.

Keywords

• fuzzy metric space
• fixed point
• binary relation
• &#8475 &#8722 <i>&#968</i>&#8722contractive mappings
• Caputo fractional differential equation