Fractional interactive fuzzy $F$-correlated Caputo-Katugampola differential equations

In this paper, we investigated the existence and uniqueness of solutions for a class of interactive fuzzy Caputo–Katugampola $F$-correlated fractional differential equations with time delay. First, we gave the definition of the correlated integral and derivative for interactive fuzzy Caputo–Katugampola $F$-correlated systems. Second, we presented an equivalent integral formulation and, under suitable assumptions, established the existence of solutions to fuzzy interactive Caputo–Katugampola $F$-correlated fractional-order differential equations with time delay by applying Schauder's fixed-point theorem. Finally, a numerical example was presented to validate the effectiveness of the proposed approach.