On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations

In this paper, orthogonal fuzzy versions are reported for some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy interpolative contractions. This way, many fixed point theorems are developed in orthogonal fuzzy metric spaces. We apply the (J,S)-fuzzy version of Banach fixed point theorem to demonstrate the existence and uniqueness of the solution. These results are supported with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.