AbstractThis research investigates the controllability of linear and non‐linear fractional dynamical systems with distributed delays in control using the ‐Caputo fractional derivative. For controllability of linear systems, the positive definiteness of Grammian matrix, which is characterized by Mittag–Leffler functions, is used to provide necessary and sufficient conditions. For the controllability of non‐linear systems, the iterative technique with the completeness of is used to obtain sufficient conditions. Using the ‐Caputo fractional derivative, this study is new since it investigates the ideas of controllability. A couple of numerical results are offered to explain the theoretical results.

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