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The goal of this study is to see if there is a solution for the fuzzy delay predator-prey system (FDPPS) with Caputo derivative. To begin, we use Schaefer's fixed point theorem to obtain results for the existence theorem of at least one solution in a Caputo FDPPS where the initial condition is also represented by a fuzzy number on fuzzy number space. We also determine the necessary and sufficient conditions of solutions for the system. Several examples are also presented to explain the oscillatory property and the existence of a solution.