Finite-time stability results for fuzzy fractional stochastic delay system under Granular differentiability concept

In present manuscript, we investigate a new type of fuzzy fractional stochastic delay system (FFSDS), in which the derivative is defined by Granular differentiability. We first transform the considered system into an equivalent integral system with the aid of fuzzy Laplace transformation and its inverse involving Mittag-Leffler function. Subsequently, existence and uniqueness results of the solutions for FFSDS are derived by applying Carath\'{e}odory approximation, under non-Lipschitz conditions, and contradiction method, respectively. \textcolor{black}{In addition, we establish the finite-time stability of the system by utilizing the generalized Gr\"{o}nwall delay inequality. Finally, the obtained conclusions are expound via an example.