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In this paper, the controllability analysis is proposed for both linear and nonlinear higher-order fractional damped stochastic dynamical systems with distributed delay in Hilbert spaces which involve fractional Caputo derivative of different orders. Based on the properties of fractional calculus, the fixed point technique, and the construction of controllability Gramian matrix, we establish the controllability results for the considered systems. Finally, examples are constructed to illustrate the applicability of obtained results.

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