A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations

This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework θ-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best proximity-point theorems for both single-valued and multivalued mappings, thereby broadening the scope of fuzzy analysis. Furthermerefore, we have for aore, we apply one of our key results to derive conditions, ensuring the existence and uniqueness of a solution to Hadamard Ψ-Caputo tempered fuzzy fractional differential equations, particularly in the context of the SIR dynamics model. These theoretical advancements are expected to open new avenues for research in fuzzy fixed-point theory and its applications to hybrid models within θ-fuzzy metric spaces.