Fixed point theorems for xi-alpha-eta-Gamma F-fuzzy contraction with an application to neutral fractional integro-differential equation with nonlocal conditions

Abstract

In this study, we define a new fuzzy contraction principle, namely, the concept of ξ-α-η-Γ F-mappings, and prove the existence and uniqueness of the fixed point for such class of mappings. To further demonstrate the validity of our results, we furnish an application to neutral fractional integro-differential equations with nonlocal conditions. The presented results unify, generalize, and enhance a number of prior findings in the literature.

Keywords

• fixed point
• fuzzy metric
• contraction
• fractional equation