Fuzzy Z-proximal contraction in strong fuzzy metric spaces

In this note, we define two distinct categories of fuzzy Z-proximal contractions and we use these two fuzzy Z-proximal contractive inequalities as a tool to obtain best proximity point for a non-self mapping which is defined between two distinct non-empty subsets of a strong fuzzy metric space. Further, prove some proximity theorems by using these categories of fuzzy Z-proximal in a complete strong fuzzy metric space. For the support of these innovative results we produce a few validation of examples. At last, we provide a solution of a non-linear second-order ordinary differential equation with the help of fuzzy Z-proximal contractive inequality provided that assumed space is strong fuzzy metric space.