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In this manuscript, we formulate the system of fuzzy stochastic fractional evolution equations (FSFEEs) driven by fractional Brownian motion. We find the results about the existence-uniqueness of the formulated system by using the Lipschitizian conditions. By using these conditions we have also investigated the exponential stability of the solution for the above system driven by fractional Brownian motion. Finally, the applications in financial mathematics are presented and the use of financial mathematics in the fractional Black and Scholes model is also discussed. An example is propounded to show the applicability of our results.