Abstract
Fixed point theory is one of the most interesting areas of research in mathematics. In this direction, we study some unique common fixed point results for a pair of self-mappings without continuity on fuzzy metric spaces under the generalized contraction conditions by using "the triangular property of fuzzy metric". Moreover, we present weak-contraction and generalized Ciric-contraction theorems. The results are supported by suitable examples. Further, we establish a supportable application of the fuzzy differential equations to ensure the existence of a unique common solution to validate our main work.